path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
GroupTheory\Index.lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Algebra.BigOperators.GroupWithZero.Finset
import Mathlib.GroupTheory.Finiteness
import Mathlib.GroupTheory.GroupAction.Quotient
/-!
# Index of a Sub... |
GroupTheory\Nilpotent.lean | /-
Copyright (c) 2021 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Ines Wright, Joachim Breitner
-/
import Mathlib.GroupTheory.Solvable
import Mathlib.GroupTheory.Sylow
import Mathlib.Algebra.Group.Subgroup.Order
/-!
# Nilpotent groups... |
GroupTheory\NoncommCoprod.lean | /-
Copyright (c) 2023 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.Algebra.Group.Commute.Hom
import Mathlib.Algebra.Group.Prod
/-!
# Canonical homomorphism from a pair of monoids
This file defines the c... |
GroupTheory\NoncommPiCoprod.lean | /-
Copyright (c) 2022 Joachim Breitner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joachim Breitner
-/
import Mathlib.GroupTheory.OrderOfElement
import Mathlib.Data.Nat.GCD.BigOperators
import Mathlib.Order.SupIndep
/-!
# Canonical homomorphism from a finite famil... |
GroupTheory\OrderOfElement.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Julian Kuelshammer
-/
import Mathlib.Algebra.CharP.Defs
import Mathlib.GroupTheory.Index
import Mathlib.Order.Interval.Set.Infinite
/-!
# Order of an element
This fil... |
GroupTheory\PGroup.lean | /-
Copyright (c) 2018 . All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Thomas Browning
-/
import Mathlib.GroupTheory.Perm.Cycle.Type
import Mathlib.GroupTheory.SpecificGroups.Cyclic
/-!
# p-groups
This file contains a proof that if `G` is a `p`-group ac... |
GroupTheory\PresentedGroup.lean | /-
Copyright (c) 2019 Michael Howes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Howes, Newell Jensen
-/
import Mathlib.GroupTheory.FreeGroup.Basic
import Mathlib.GroupTheory.QuotientGroup
/-!
# Defining a group given by generators and relations
Given a su... |
GroupTheory\PushoutI.lean | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.GroupTheory.CoprodI
import Mathlib.GroupTheory.Coprod.Basic
import Mathlib.GroupTheory.Complement
/-!
## Pushouts of Monoids and Groups
This file defin... |
GroupTheory\QuotientGroup.lean | /-
Copyright (c) 2018 Kevin Buzzard, Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Patrick Massot
This file is to a certain extent based on `quotient_module.lean` by Johannes Hölzl.
-/
import Mathlib.Algebra.Group.Subgroup.Finite
import... |
GroupTheory\Schreier.lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.GroupTheory.Abelianization
import Mathlib.GroupTheory.Transfer
/-!
# Schreier's Lemma
In this file we prove Schreier's lemma.
## Main results
- `... |
GroupTheory\SchurZassenhaus.lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.GroupTheory.Transfer
/-!
# The Schur-Zassenhaus Theorem
In this file we prove the Schur-Zassenhaus theorem.
## Main results
- `exists_right_compl... |
GroupTheory\SemidirectProduct.lean | /-
Copyright (c) 2020 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Group.Subgroup.Basic
/-!
# Semidirect product
This file defines semidirect products of groups, and the canonical maps in and out of the
semidirec... |
GroupTheory\Solvable.lean | /-
Copyright (c) 2021 Jordan Brown, Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jordan Brown, Thomas Browning, Patrick Lutz
-/
import Mathlib.GroupTheory.Abelianization
import Mathlib.GroupTheory.Perm.ViaEmbedding
import Mathlib.GroupT... |
GroupTheory\Sylow.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Thomas Browning
-/
import Mathlib.Data.SetLike.Fintype
import Mathlib.GroupTheory.PGroup
import Mathlib.GroupTheory.NoncommPiCoprod
/-!
# Sylow theorems
The Sylow theorem... |
GroupTheory\Torsion.lean | /-
Copyright (c) 2022 Julian Berman. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Berman
-/
import Mathlib.GroupTheory.PGroup
/-!
# Torsion groups
This file defines torsion groups, i.e. groups where all elements have finite order.
## Main definitions
* `Mo... |
GroupTheory\Transfer.lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.GroupTheory.Complement
import Mathlib.GroupTheory.Sylow
/-!
# The Transfer Homomorphism
In this file we construct the transfer homomorphism.
## Ma... |
GroupTheory\Congruence\Basic.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.Submonoid.Operations
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Data.... |
GroupTheory\Congruence\BigOperators.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.GroupTheory.Congruence.Basic
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Multiset
import Mathlib.... |
GroupTheory\Congruence\Opposite.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.GroupTheory.Congruence.Basic
import Mathlib.Algebra.Opposites
/-!
# Congruences on the opposite of a group
This file defines the order isomorp... |
GroupTheory\Coprod\Basic.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.Algebra.PUnitInstances.Algebra
import Mathlib.GroupTheo... |
GroupTheory\Coxeter\Basic.lean | /-
Copyright (c) 2024 Newell Jensen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Newell Jensen, Mitchell Lee
-/
import Mathlib.Algebra.Ring.Int
import Mathlib.GroupTheory.PresentedGroup
import Mathlib.GroupTheory.Coxeter.Matrix
import Mathlib.Tactic.Ring
import Math... |
GroupTheory\Coxeter\Inversion.lean | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee
-/
import Mathlib.GroupTheory.Coxeter.Length
import Mathlib.Data.ZMod.Parity
import Mathlib.Data.List.GetD
/-!
# Reflections, inversions, and inversion sequences
Throughou... |
GroupTheory\Coxeter\Length.lean | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee
-/
import Mathlib.Data.ZMod.Basic
import Mathlib.GroupTheory.Coxeter.Basic
import Mathlib.Tactic.Zify
/-!
# The length function, reduced words, and descents
Throughout thi... |
GroupTheory\Coxeter\Matrix.lean | /-
Copyright (c) 2024 Newell Jensen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Newell Jensen, Mitchell Lee
-/
import Mathlib.Data.Matrix.Notation
import Mathlib.LinearAlgebra.Matrix.Symmetric
/-!
# Coxeter matrices
Let us say that a matrix (possibly an infinite ... |
GroupTheory\FreeGroup\Basic.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.List.Sublists
import Mathlib.Data.List.InsertNth
/-!
# Free groups
This file... |
GroupTheory\FreeGroup\IsFreeGroup.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn, Eric Wieser, Joachim Breitner
-/
import Mathlib.GroupTheory.FreeGroup.Basic
/-!
# Free groups structures on arbitrary types
This file defines the notion of free basis of a gr... |
GroupTheory\FreeGroup\NielsenSchreier.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.CategoryTheory.Action
import Mathlib.Combinatorics.Quiver.Arborescence
import Mathlib.Combinatorics.Quiver.ConnectedComponent
import Mathlib.GroupTheory.FreeGr... |
GroupTheory\GroupAction\Basic.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Data.Fintype.Card
import Mathlib.Data.Set.Finite
import Mathli... |
GroupTheory\GroupAction\BigOperators.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Data.Finset.Basic
import Mathlib.Data.Multiset.Basi... |
GroupTheory\GroupAction\Blocks.lean | /-
Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.Data.Setoid.Partition
import Mathlib.GroupTheory.GroupAction.Basic
import Mathlib.GroupTheory.GroupAction.Pointwise
import Mathlib.Group... |
GroupTheory\GroupAction\ConjAct.lean | /-
Copyright (c) 2021 . All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.Group.Subgroup.ZPowers
import Mathlib.Algebra.Ring.Action.Basic
import Mathlib.GroupTheory.GroupAction.Basic
/-!
# Conjugati... |
GroupTheory\GroupAction\Embedding.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Basic
import Mathlib.Algebra.Group.Action.Pi
/-!
# Group actions on embeddings
This file provides a `MulAction G (α ↪ β)` instance tha... |
GroupTheory\GroupAction\FixedPoints.lean | /-
Copyright (c) 2024 Emilie Burgun. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Emilie Burgun
-/
import Mathlib.Algebra.Group.Commute.Basic
import Mathlib.GroupTheory.GroupAction.Basic
import Mathlib.Dynamics.PeriodicPts
import Mathlib.Data.Set.Pointwise.SMul
/-!
... |
GroupTheory\GroupAction\FixingSubgroup.lean | /-
Copyright (c) 2022 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.Algebra.Group.Subgroup.Actions
import Mathlib.GroupTheory.GroupAction.Basic
import Mathlib.GroupTheory.GroupAction.FixedPoints
/-!
# Fi... |
GroupTheory\GroupAction\Group.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Group.Action.Basic
import Mathlib.Algebra.Group.Aut
import Mathlib.Algebra.Group.Invertible.Basic
import Mathlib.Algebra.GroupWithZero.Action.Units... |
GroupTheory\GroupAction\Hom.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Antoine Chambert-Loir
-/
import Mathlib.Algebra.Module.Defs
import Mathlib.Algebra.Ring.Action.Basic
import Mathlib.Algebra.Group.Hom.CompTypeclasses
/-!
# Equivariant homomor... |
GroupTheory\GroupAction\IterateAct.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Ring.Nat
import Mathlib.Algebra.Group.Action.Defs
/-!
# Monoid action by iterates of a map
In this file we define `IterateMulAct f`, `f : α... |
GroupTheory\GroupAction\Period.lean | /-
Copyright (c) 2024 Emilie Burgun. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Emilie Burgun
-/
import Mathlib.Dynamics.PeriodicPts
import Mathlib.GroupTheory.Exponent
import Mathlib.GroupTheory.GroupAction.Basic
/-!
# Period of a group action
This module defin... |
GroupTheory\GroupAction\Pointwise.lean | /-
Copyright (c) 2024 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro, Anne Baanen,
Frédéric Dupuis, Heather Macbeth, Antoine Chambert-Loir
-/
import Mathlib.Data.Set.Pointwise.SMul
impor... |
GroupTheory\GroupAction\Quotient.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Thomas Browning
-/
import Mathlib.Algebra.Group.ConjFinite
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Dynamics.PeriodicPts
import Mathlib.GroupTheory.Commutato... |
GroupTheory\GroupAction\Ring.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Algebra.Ring.Defs
/-!
# Commutativity and associativity of action of integers on rings
This file proves that `ℕ` a... |
GroupTheory\GroupAction\SubMulAction.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Module.Defs
import Mathlib.Data.SetLike.Basic
import Mathlib.GroupTheory.GroupAction.Basic
import Mathlib.GroupTheory.GroupAction.Hom
/-!
# Sets in... |
GroupTheory\GroupAction\Support.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Set.Pointwise.SMul
/-!
# Support of an element under an action action
Given an action of a group `G` on a type `α`, we say that a set `s : Set α` su... |
GroupTheory\GroupAction\DomAct\ActionHom.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.GroupTheory.GroupAction.DomAct.Basic
import Mathlib.GroupTheory.GroupAction.Hom
/-!
# Action of `Mᵈᵐᵃ` on `α →[N] β` and `A →+[N] B`
In this file we... |
GroupTheory\GroupAction\DomAct\Basic.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Group.Opposite
import Mathlib.Algebra.Group.Pi.Lemmas
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Algebra.Ring.Defs
/-!
... |
GroupTheory\GroupAction\SubMulAction\Pointwise.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.GroupTheory.GroupAction.SubMulAction
/-!
# Pointwise monoid structures on SubMulAction
This file provides `SubMulAction.Monoid` and weaker typeclasses, whi... |
GroupTheory\MonoidLocalization\Basic.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.GroupTheory.Congruence.Basic
import Mathlib.RingTheory.OreLocalization.Basic
/-!
# Localizatio... |
GroupTheory\MonoidLocalization\MonoidWithZero.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Regular.Basic
import Mathlib.GroupTheory.MonoidLocalization.Basic
/-!
# Localizations of commutative monoids with zeroes
-/
open Funct... |
GroupTheory\MonoidLocalization\Order.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.GroupTheory.MonoidLocalization.Basic
/-!
# Ordered structures on localizations of commutative monoids
-/
open Function
namespace Localization... |
GroupTheory\Order\Min.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.GroupTheory.Torsion
/-!
# Minimum order of an element
This file defines the minimum order of an element of a monoid.
## Main declarations
* `Monoid.min... |
GroupTheory\Perm\Basic.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
import Mathlib.Algebra.Group.Prod
import Mathlib.Algebra.Group.Units.Equiv
import Mathlib.Algebra.GroupPower.IterateHom
import Mathlib.Logic... |
GroupTheory\Perm\Closure.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yaël Dillies
-/
import Mathlib.GroupTheory.Perm.Cycle.Basic
/-!
# Closure results for permutation groups
* This file contains several closure results:
* `closure_isCycle... |
GroupTheory\Perm\ClosureSwap.lean | /-
Copyright (c) 2024 Thomas Browning, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Junyan Xu
-/
import Mathlib.Data.Set.Finite
import Mathlib.GroupTheory.GroupAction.FixedPoints
import Mathlib.GroupTheory.Perm.Support
/-!
# Subgroups gen... |
GroupTheory\Perm\DomMulAct.lean | /-
Copyright (c) 2023 Junyan Xu, Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu, Antoine Chambert-Loir
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.GroupTheory.GroupAction.DomAct.Basic
import Mathlib.GroupTheory.GroupAc... |
GroupTheory\Perm\Fin.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.GroupTheory.Perm.Cycle.Type
import Mathlib.GroupTheory.Perm.Option
import Mathlib.Logic.Equiv.Fin
import Mathlib.Logic.Equiv.Fintype
/-!
# Permutations of `... |
GroupTheory\Perm\Finite.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Data.Finset.Fin
import Mathlib.Data.Int.Order.Units
import Mathlib.GroupTheory.OrderOfElement
import Mathlib.GroupTheory.Perm.Support
import Mathlib.Logic.... |
GroupTheory\Perm\List.lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Data.List.Rotate
import Mathlib.GroupTheory.Perm.Support
/-!
# Permutations from a list
A list `l : List α` ... |
GroupTheory\Perm\Option.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Data.Fintype.Option
import Mathlib.Data.Fintype.Perm
import Mathlib.Data.Fintype.Prod
import Mathlib.GroupTheory.Perm.Sign
import Mathlib.Logic.Equiv.Option
... |
GroupTheory\Perm\Sign.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.Data.Finset.Fin
import Mathlib.Data.Finset.Sort
import Mathli... |
GroupTheory\Perm\Subgroup.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Basic
import Mathlib.Algebra.Group.Subgroup.Finite
import Mathlib.Data.Fintype.Perm
import Mathlib.GroupTheory.Perm.Basic
/-!
# Lemmas ... |
GroupTheory\Perm\Support.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Aaron Anderson, Yakov Pechersky
-/
import Mathlib.Algebra.Group.Commute.Basic
import Mathlib.Data.Fintype.Card
import Mathlib.GroupTheory.Perm.Basic
/-!
# support of a per... |
GroupTheory\Perm\ViaEmbedding.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
import Mathlib.GroupTheory.Perm.Basic
import Mathlib.Logic.Equiv.Set
/-!
# `Equiv.Perm.viaEmbedding`, a noncomputable analogue of `Equiv.Pe... |
GroupTheory\Perm\Cycle\Basic.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yaël Dillies
-/
import Mathlib.Algebra.Module.BigOperators
import Mathlib.Data.Fintype.Perm
import Mathlib.GroupTheory.Perm.Finite
import Mathlib.GroupTheory.Perm.List
/-... |
GroupTheory\Perm\Cycle\Concrete.lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Data.List.Cycle
import Mathlib.GroupTheory.Perm.Cycle.Type
import Mathlib.GroupTheory.Perm.List
/-!
# Properties of cyclic permutations constructed... |
GroupTheory\Perm\Cycle\Factors.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yaël Dillies
-/
import Mathlib.Algebra.Module.BigOperators
import Mathlib.Data.Finset.NoncommProd
import Mathlib.Data.Fintype.Perm
import Mathlib.Data.Int.ModEq
import Mat... |
GroupTheory\Perm\Cycle\PossibleTypes.lean | /-
Copyright (c) 2023 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.GroupTheory.Perm.Cycle.Concrete
/-! # Possible cycle types of permutations
* For `m : Multiset ℕ`, `Equiv.Perm.exists_with_cycleType_i... |
GroupTheory\Perm\Cycle\Type.lean | /-
Copyright (c) 2020 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Algebra.GCDMonoid.Multiset
import Mathlib.Combinatorics.Enumerative.Partition
import Mathlib.Data.List.Rotate
import Mathlib.GroupTheory.Perm.Cycle.F... |
GroupTheory\SpecificGroups\Alternating.lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Algebra.Group.ConjFinite
import Mathlib.GroupTheory.Perm.Fin
import Mathlib.GroupTheory.Subgroup.Simple
import Mathlib.Tactic.IntervalCases
/-!
# Alte... |
GroupTheory\SpecificGroups\Cyclic.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Data.Nat.Totient
import Mathlib.Data.ZMod.Quotient
import Mathlib.GroupTheory.OrderOfElement
impo... |
GroupTheory\SpecificGroups\Dihedral.lean | /-
Copyright (c) 2020 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import Mathlib.Data.ZMod.Basic
import Mathlib.GroupTheory.Exponent
/-!
# Dihedral Groups
We define the dihedral groups `DihedralGroup n`, with elements `r i` and `sr ... |
GroupTheory\SpecificGroups\KleinFour.lean | /-
Copyright (c) 2023 Newell Jensen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Newell Jensen
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.GroupTheory.SpecificGroups.Dihedral
/-!
# Klein Four Group
The Klein (Vierergruppe) four-group is a no... |
GroupTheory\SpecificGroups\Quaternion.lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import Mathlib.Data.ZMod.Basic
import Mathlib.Algebra.Group.Nat
import Mathlib.Tactic.IntervalCases
import Mathlib.GroupTheory.SpecificGroups.Dihedral
import ... |
GroupTheory\Subgroup\Center.lean | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Algebra.GroupWithZero.Units.Basic
import Mathlib.GroupTheory.Submonoid.Center
/-!
# Centers of subgroups
-/
o... |
GroupTheory\Subgroup\Centralizer.lean | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.GroupTheory.Subgroup.Center
import Mathlib.GroupTheory.Submonoid.Centralizer
/-!
# Centralizers of subgroups
-/
open Function
open Int
variable {G : Type... |
GroupTheory\Subgroup\Saturated.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Algebra.Module.Defs
/-!
# Saturated subgroups
## Tags
subgroup, subgroups
-/
namespace Subgroup
varia... |
GroupTheory\Subgroup\Simple.lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Order.Atoms
import Mathlib.Algebra.Group.Subgroup.Basic
/-!
# Simple groups
This file defines `IsSimpleGroup G`, a class indicating that a group has ... |
GroupTheory\Submonoid\Center.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Submonoid.Operations
import Mathlib.GroupTheory.Subsemigroup.Center
/-!
# Centers of monoids
## Main definitions
* `Submonoid.center`: the c... |
GroupTheory\Submonoid\Centralizer.lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.GroupTheory.Subsemigroup.Centralizer
import Mathlib.GroupTheory.Submonoid.Center
/-!
# Centralizers of magmas and monoids
## Main definitions
* `S... |
GroupTheory\Submonoid\Inverses.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Algebra.Group.Submonoid.Pointwise
/-!
# Submonoid of inverses
Given a submonoid `N` of a monoid `M`, we define the submonoid `N.leftInv` as the submonoid ... |
GroupTheory\Subsemigroup\Center.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Jireh Loreaux
-/
import Mathlib.Algebra.Group.Center
import Mathlib.Algebra.Group.Subsemigroup.Operations
/-!
# Centers of semigroups, as subsemigroups.
## Main definitions... |
GroupTheory\Subsemigroup\Centralizer.lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Jireh Loreaux
-/
import Mathlib.GroupTheory.Subsemigroup.Center
import Mathlib.Algebra.Group.Center
/-!
# Centralizers in semigroups, as subsemigroups.
## Main defi... |
InformationTheory\Hamming.lean | /-
Copyright (c) 2022 Wrenna Robson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wrenna Robson
-/
import Mathlib.Analysis.Normed.Group.Basic
import Mathlib.Topology.Instances.Discrete
/-!
# Hamming spaces
The Hamming metric counts the number of places two members ... |
Init\Classical.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import Mathlib.Tactic.IrreducibleDef
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers from the por... |
Init\Core.lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
import Mathlib.Tactic.Relation.Trans
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers from the port from Mathlib3... |
Init\Logic.lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
-/
import Mathlib.Tactic.Lemma
import Mathlib.Tactic.Relation.Trans
import Mathlib.Tactic.ProjectionNotation
import Batteries.... |
Init\Quot.lean | /-
Copyright (c) 2023 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers from the port from Mathlib3.
(They contain content moved from lean3 itself that Mat... |
Init\Set.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Parser.Term
import Batteries.Util.ExtendedBinder
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers from the port from ... |
Init\Algebra\Classes.lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Init.Logic
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers from the port from Mathlib3.
(They contain content mov... |
Init\Data\Quot.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers from the port from Mathlib3.
(They contain content moved from lean3 itself that ... |
Init\Data\Fin\Basic.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Data.Nat.Notation
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers from the port from Mathlib3.
(They contain cont... |
Init\Data\Int\Order.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Data.Int.Notation
import Mathlib.Data.Nat.Notation
import Mathlib.Order.Defs
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers... |
Init\Data\List\Basic.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Data.Nat.Notation
import Batteries.Data.List.Basic
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers from the port ... |
Init\Data\List\Instances.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers from the port from Mathlib3.
(They contain content moved from lean3 itself that ... |
Init\Data\List\Lemmas.lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn
-/
import Batteries.Data.List.Lemmas
import Mathlib.Tactic.Cases
/-!
# Note about `Mathlib/Init/`
The files in `... |
Init\Data\Nat\Lemmas.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
-/
import Batteries.Data.Nat.Lemmas
import Batteries.WF
import Mathlib.Util.AssertExists
import Mathlib.Data.Nat.Notation
/-!
# Note about `Mat... |
Init\Data\Sigma\Basic.lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
-/
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers from the port from Mathlib3.
(They contain cont... |
Init\Data\Sigma\Lex.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers from the port from Mathlib3.
(They contain content moved from lean3 itself that ... |
Init\Order\LinearOrder.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import Mathlib.Order.Defs
/-!
# Note about `Mathlib/Init/`
The files in `Mathlib/Init` are leftovers from the port from Mathlib3.
(They cont... |
Lean\CoreM.lean | /-
Copyright (c) 2023 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Tactic.ToExpr
/-!
# Additional functions using `CoreM` state.
-/
open Lean Core
/--
Run a `CoreM α` in a fresh `Environment` with specified `modules... |
Lean\EnvExtension.lean | /-
Copyright (c) 2023 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Lean.ScopedEnvExtension
/-!
# Helper function for environment extensions and attributes.
-/
open Lean
instance {σ : Type} [Inhabited σ] : Inhabited (Sco... |
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