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"differentiability class. summary. parametric _ continuity. in mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called differentiability class. at the very minimum, a function could be considered smooth if it is differentiable ev... |
"spaces of test functions and distributions. summary. spaces _ of _ test _ functions _ and _ distributions. in mathematical analysis, the spaces of test functions and distributions are topological vector spaces ( tvss ) that are used in the definition and application of distributions. test functions are usually infinit... |
"spaces of test functions and distributions. summary. spaces _ of _ test _ functions _ and _ distributions. there are other possible choices for the space of test functions, which lead to other different spaces of distributions. if u = r n { \ displaystyle u = \ mathbb { r } ^ { n } } then the use of schwartz functions... |
"spaces of test functions and distributions. summary. spaces _ of _ test _ functions _ and _ distributions. the set of tempered distributions forms a vector subspace of the space of distributions d β² ( u ) { \ displaystyle { \ mathcal { d } } ^ { \ prime } ( u ) } and is thus one example of a space of distributions ; t... |
"staircase paradox. summary. staircase _ paradox. in mathematical analysis, the staircase paradox is a pathological example showing that limits of curves do not necessarily preserve their length. it consists of a sequence of "" staircase "" polygonal chains in a unit square, formed from horizontal and vertical line seg... |
"staircase paradox. summary. staircase _ paradox. it shows that, for curves under uniform convergence, the length of a curve is not a continuous function of the curve. for any smooth curve, polygonal chains with segment lengths decreasing to zero, connecting consecutive vertices along the curve, always converge to the ... |
"chebyshev norm. summary. uniform _ metric. in mathematical analysis, the uniform norm ( or sup norm ) assigns to real - or complex - valued bounded functions f { \ displaystyle f } defined on a set s { \ displaystyle s } the non - negative number β f β β = β f β β, s = sup { | f ( s ) | : s β s }. { \ displaystyle \ |... |
"chebyshev norm. summary. uniform _ metric. the name "" uniform norm "" derives from the fact that a sequence of functions { f n } { \ displaystyle \ left \ { f _ { n } \ right \ } } converges to f { \ displaystyle f } under the metric derived from the uniform norm if and only if f n { \ displaystyle f _ { n } } conver... |
"universal chord theorem. summary. universal _ chord _ theorem. in mathematical analysis, the universal chord theorem states that if a function f is continuous on and satisfies f ( a ) = f ( b ) { \ displaystyle f ( a ) = f ( b ) }, then for every natural number n { \ displaystyle n }, there exists some x β { \ display... |
"multimedia. mathematical and scientific research. multi _ format _ publishing > usage / application > mathematical and scientific research. in mathematical and scientific research, multimedia is mainly used for modeling and simulation. for example, a scientist can look at a molecular model of a particular substance an... |
"multimedia. mathematical and scientific research. multi _ format _ publishing > usage / application > mathematical and scientific research. one well known example of this being applied would be in the movie interstellar where executive director kip thorne helped create one of the most realistic depictions of a blackho... |
"q - pochhammer symbol. summary. q - pochhammer _ symbol. in mathematical area of combinatorics, the q - pochhammer symbol, also called the q - shifted factorial, is the product with ( a ; q ) 0 = 1. { \ displaystyle ( a ; q ) _ { 0 } = 1. } it is a q - analog of the pochhammer symbol ( x ) n = x ( x + 1 ) β¦ ( x + n β ... |
"community matrix. summary. community _ matrix. in mathematical biology, the community matrix is the linearization of a generalized lotka β volterra equation at an equilibrium point. the eigenvalues of the community matrix determine the stability of the equilibrium point. for example, the lotka β volterra predator β pr... |
"community matrix. summary. community _ matrix. by the hartman β grobman theorem the non - linear system is topologically equivalent to a linearization of the system about an equilibrium point ( x *, y * ), which has the form = a, { \ displaystyle { \ begin { bmatrix } { \ frac { du } { dt } } \ \ { \ frac { dv } { dt ... |
"pauline van den driessche. contributions. pauline _ van _ den _ driessche > contributions. in mathematical biology, van den driessche's contributions include important work on delay differential equations and on hopf bifurcations, and the effects of changing population size and immigration on epidemics. she has also d... |
"transylvania lottery. summary. transylvania _ lottery. in mathematical combinatorics, the transylvania lottery is a lottery where players selected three numbers from 1 - 14 for each ticket, and then three numbers are chosen randomly. a ticket wins if two of the numbers match the random ones. the problem asks how many ... |
"transylvania lottery. summary. transylvania _ lottery. each set of seven uses every line of a fano plane, labelled with the numbers 1 to 7, and 8 to 14. at least two of the three randomly chosen numbers must be in one fano plane set, and any two points on a fano plane are on a line, so there will be a ticket in the co... |
"rado's theorem ( riemann surfaces ). summary. rado's _ theorem _ ( riemann _ surfaces ). in mathematical complex analysis, rado's theorem, proved by tibor rado ( 1925 ), states that every connected riemann surface is second - countable ( has a countable base for its topology ). the prufer surface is an example of a su... |
"schottky theorem. summary. schottky _ theorem. in mathematical complex analysis, schottky's theorem, introduced by schottky ( 1904 ) is a quantitative version of picard's theorem. it states that for a holomorphic function f in the open unit disk that does not take the values 0 or 1, the value of | f ( z ) | can be bou... |
"quasiconformal map. summary. quasi - conformal _ mapping. in mathematical complex analysis, a quasiconformal mapping, introduced by grotzsch ( 1928 ) and named by ahlfors ( 1935 ), is a homeomorphism between plane domains which to first order takes small circles to small ellipses of bounded eccentricity. intuitively, ... |
"geometric function theory. quasiconformal maps. geometric _ function _ theory > topics in geometric function theory > quasiconformal maps. in mathematical complex analysis, a quasiconformal mapping, introduced by grotzsch ( 1928 ) and named by ahlfors ( 1935 ), is a homeomorphism between plane domains which to first o... |
"universal teichmuller space. summary. universal _ teichmuller _ space. in mathematical complex analysis, universal teichmuller space t ( 1 ) is a teichmuller space containing the teichmuller space t ( g ) of every fuchsian group g. it was introduced by bers ( 1965 ) as the set of boundary values of quasiconformal maps... |
"kleinian integer. summary. kleinian _ integer. in mathematical cryptography, a kleinian integer is a complex number of the form m + n 1 + β 7 2 { \ displaystyle m + n { \ frac { 1 + { \ sqrt { - 7 } } } { 2 } } }, with m and n rational integers. they are named after felix klein. the kleinian integers form a ring calle... |
"semi colon. mathematics. semi _ colon > mathematics. in the calculus of relations, the semicolon is used in infix notation for the composition of relations : a ; b = { ( x, z ) : y x a y β§ y b z }. { \ displaystyle a ; b \ = \ \ { ( x, z ) : \ exists y \ \ xay \ \ land \ ybz \ } ~. } the ; humphrey point is sometimes ... |
"continuous - time signal. summary. continuous _ time. in mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled." |
"topkis's theorem. summary. topkis's _ theorem. in mathematical economics, topkis's theorem is a result that is useful for establishing comparative statics. the theorem allows researchers to understand how the optimal value for a choice variable changes when a feature of the environment changes. the result states that ... |
"isoelastic function. summary. isoelastic _ function. in mathematical economics, an isoelastic function, sometimes constant elasticity function, is a function that exhibits a constant elasticity, i. e. has a constant elasticity coefficient. the elasticity is the ratio of the percentage change in the dependent variable ... |
"applied general equilibrium. summary. applied _ general _ equilibrium. in mathematical economics, applied general equilibrium ( age ) models were pioneered by herbert scarf at yale university in 1967, in two papers, and a follow - up book with terje hansen in 1973, with the aim of empirically estimating the arrow β de... |
"applied general equilibrium. summary. applied _ general _ equilibrium. scarf never built an age model, but hinted that β these novel numerical techniques might be useful in assessing consequences for the economy of a change in the economic environment β ( kehoe et al. 2005, citing scarf 1967b ). his students elaborate... |
"applied general equilibrium. summary. applied _ general _ equilibrium. earlier analytic work with these models has examined the distortionary effects of taxes, tariffs, and other policies, along with functional incidence questions. more recent applied models, including those discussed here, provide numerical estimates... |
"applied general equilibrium. summary. applied _ general _ equilibrium. scarf's fixed - point method was a break - through in the mathematics of computation generally, and specifically in optimization and computational economics. later researchers continued to develop iterative methods for computing fixed - points, bot... |
"arrow β debreu model. summary. arrow β debreu _ model. in mathematical economics, the arrow β debreu model is a theoretical general equilibrium model. it posits that under certain economic assumptions ( convex preferences, perfect competition, and demand independence ) there must be a set of prices such that aggregate... |
"arrow β debreu model. summary. arrow β debreu _ model. in general, there may be many equilibria. arrow ( 1972 ) and debreu ( 1983 ) were separately awarded the nobel prize in economics for their development of the model. mckenzie however was not awarded." |
"solomon mikhlin. elasticity theory and boundary value problems. solomon _ mikhlin > work > research activity > elasticity theory and boundary value problems. in mathematical elasticity theory, mikhlin was concerned by three themes : the plane problem ( mainly from 1932 to 1935 ), the theory of shells ( from 1954 ) and... |
"solomon mikhlin. elasticity theory and boundary value problems. solomon _ mikhlin > work > research activity > elasticity theory and boundary value problems. mikhlin studied its convergence and gave applications to special applied problems. he proved existence theorems for the fundamental problems of plane elasticity ... |
"solomon mikhlin. elasticity theory and boundary value problems. solomon _ mikhlin > work > research activity > elasticity theory and boundary value problems. he studied the error of the approximate solution for shells, similar to plane plates, and found out that this error is small for the so - called purely rotationa... |
"solomon mikhlin. elasticity theory and boundary value problems. solomon _ mikhlin > work > research activity > elasticity theory and boundary value problems. mikhlin studied also the spectrum of the operator pencil of the classical linear elastostatic operator or navier β cauchy operator a ( Ο ) u = Ξ΄ 2 u + Ο β ( β β
... |
"corner angle. identifying angles. reflex _ angle > identifying angles. in mathematical expressions, it is common to use greek letters ( Ξ±, Ξ², Ξ³, ΞΈ, Ο,... )" |
"corner angle. identifying angles. reflex _ angle > identifying angles. as variables denoting the size of some angle ( to avoid confusion with its other meaning, the symbol Ο is typically not used for this purpose ). lower case roman letters ( a, b, c,.." |
"corner angle. identifying angles. reflex _ angle > identifying angles.. ) are also used. in contexts where this is not confusing, an angle may be denoted by the upper case roman letter denoting its vertex." |
"corner angle. identifying angles. reflex _ angle > identifying angles. see the figures in this article for examples. the three defining points may also identify angles in geometric figures. for example, the angle with vertex a formed by the rays ab and ac ( that is, the half - lines from point a through points b and c... |
"corner angle. identifying angles. reflex _ angle > identifying angles. where there is no risk of confusion, the angle may sometimes be referred to by a single vertex alone ( in this case, "" angle a "" ). potentially, an angle denoted as, say, might refer to any of four angles : the clockwise angle from b to c about a... |
"littlewood β offord problem. summary. littlewood β offord _ problem. in mathematical field of combinatorial geometry, the littlewood β offord problem is the problem of determining the number of subsums of a set of vectors that fall in a given convex set. more formally, if v is a vector space of dimension d, the proble... |
"littlewood β offord problem. summary. littlewood β offord _ problem. this bound is sharp ; equality is attained when all vectors in s are equal. in 1966, kleitman showed that the same bound held for complex numbers. in 1970, he extended this to the setting when v is a normed space. suppose s = { v1, β¦, vn }." |
"littlewood β offord problem. summary. littlewood β offord _ problem. by subtracting 1 2 i = 1 n v i { \ displaystyle { \ frac { 1 } { 2 } } \ sum _ { i = 1 } ^ { n } v _ { i } } from each possible subsum ( that is, by changing the origin and then scaling by a factor of 2 ), the littlewood β offord problem is equivalen... |
"pseudoreal representation. summary. pseudoreal _ representation. in mathematical field of representation theory, a quaternionic representation is a representation on a complex vector space v with an invariant quaternionic structure, i. e., an antilinear equivariant map j : v β v { \ displaystyle j \ colon v \ to v } w... |
"pseudoreal representation. summary. pseudoreal _ representation. from this point of view, quaternionic representation of a group g is a group homomorphism Ο : g β gl ( v, h ), the group of invertible quaternion - linear transformations of v. in particular, a quaternionic matrix representation of g assigns a square mat... |
"symplectic representation. summary. symplectic _ representation. in mathematical field of representation theory, a symplectic representation is a representation of a group or a lie algebra on a symplectic vector space ( v, Ο ) which preserves the symplectic form Ο. here Ο is a nondegenerate skew symmetric bilinear for... |
"smoluchowski equation. particular cases with known solution and inversion. smoluchowski _ equation > particular cases with known solution and inversion. in mathematical finance for volatility smile modeling of options via local volatility, one has the problem of deriving a diffusion coefficient Ο ( x t, t ) { \ displa... |
"margrabe's formula. summary. margrabe's _ formula. in mathematical finance, margrabe's formula is an option pricing formula applicable to an option to exchange one risky asset for another risky asset at maturity. it was derived by william margrabe ( phd chicago ) in 1978. margrabe's paper has been cited by over 2000 s... |
"monte carlo option model. summary. monte _ carlo _ methods _ for _ option _ pricing. in mathematical finance, a monte carlo option model uses monte carlo methods to calculate the value of an option with multiple sources of uncertainty or with complicated features. the first application to option pricing was by phelim ... |
"replicating portfolio. summary. replicating _ portfolio. in mathematical finance, a replicating portfolio for a given asset or series of cash flows is a portfolio of assets with the same properties ( especially cash flows ). this is meant in two distinct senses : static replication, where the portfolio has the same ca... |
"replicating portfolio. summary. replicating _ portfolio. the notion of a replicating portfolio is fundamental to rational pricing, which assumes that market prices are arbitrage - free β concretely, arbitrage opportunities are exploited by constructing a replicating portfolio. in practice, replicating portfolios are s... |
"equivalent martingale measure. summary. martingale _ measure. in mathematical finance, a risk - neutral measure ( also called an equilibrium measure, or equivalent martingale measure ) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measu... |
"convexity ( finance ). summary. convexity _ correction. in mathematical finance, convexity refers to non - linearities in a financial model. in other words, if the price of an underlying variable changes, the price of an output does not change linearly, but depends on the second derivative ( or, loosely speaking, high... |
"kelly criterion. application to the stock market. kelly _ criterion > application to the stock market. in mathematical finance, if security weights maximize the expected geometric growth rate ( which is equivalent to maximizing log wealth ), then a portfolio is growth optimal. computations of growth optimal portfolios... |
"kelly criterion. application to the stock market. kelly _ criterion > application to the stock market. if portfolio weights are largely a function of estimation errors, then ex - post performance of a growth - optimal portfolio may differ fantastically from the ex - ante prediction. parameter uncertainty and estimatio... |
"black - scholes equation. summary. black β scholes _ equation. in mathematical finance, the black β scholes equation is a partial differential equation ( pde ) governing the price evolution of a european call or european put under the black β scholes model. broadly speaking, the term may refer to a similar pde that ca... |
"constant elasticity of variance model. summary. constant _ elasticity _ of _ variance _ model. in mathematical finance, the cev or constant elasticity of variance model is a stochastic volatility model that attempts to capture stochastic volatility and the leverage effect. the model is widely used by practitioners in ... |
"cox β ingersoll β ross model. summary. cir _ process. in mathematical finance, the cox β ingersoll β ross ( cir ) model describes the evolution of interest rates. it is a type of "" one factor model "" ( short - rate model ) as it describes interest rate movements as driven by only one source of market risk. the model... |
"doob decomposition theorem. application. doob _ decomposition _ theorem > application. in mathematical finance, the doob decomposition theorem can be used to determine the largest optimal exercise time of an american option. let x = ( x0, x1,..." |
"doob decomposition theorem. application. doob _ decomposition _ theorem > application., xn ) denote the non - negative, discounted payoffs of an american option in a n - period financial market model, adapted to a filtration ( f0, f1,..." |
"doob decomposition theorem. application. doob _ decomposition _ theorem > application., fn ), and let q { \ displaystyle \ mathbb { q } } denote an equivalent martingale measure. let u = ( u0, u1,.." |
"doob decomposition theorem. application. doob _ decomposition _ theorem > application.., un ) denote the snell envelope of x with respect to q { \ displaystyle \ mathbb { q } }. the snell envelope is the smallest q { \ displaystyle \ mathbb { q } } - supermartingale dominating x and in a complete financial market it r... |
"doob decomposition theorem. application. doob _ decomposition _ theorem > application. let u = m + a denote the doob decomposition with respect to q { \ displaystyle \ mathbb { q } } of the snell envelope u into a martingale m = ( m0, m1,..." |
"doob decomposition theorem. application. doob _ decomposition _ theorem > application., mn ) and a decreasing predictable process a = ( a0, a1,..." |
"doob decomposition theorem. application. doob _ decomposition _ theorem > application., an ) with a0 = 0. then the largest stopping time to exercise the american option in an optimal way is Ο max : = { n if a n = 0, min { n β { 0, β¦, n β 1 } a n + 1 < 0 } if a n < 0. { \ displaystyle \ tau _ { \ text { max } } : = { \... |
"doob decomposition theorem. application. doob _ decomposition _ theorem > application..., n β 1 }, hence Οmax is indeed a stopping time. it gives the last moment before the discounted value of the american option will drop in expectation ; up to time Οmax the discounted value process u is a martingale with respect to ... |
"option delta. summary. greeks _ ( finance ). in mathematical finance, the greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. the name is used beca... |
"sabr volatility model. summary. sabr _ volatility _ model. in mathematical finance, the sabr model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. the name stands for "" stochastic alpha, beta, rho "", referring to the parameters of the model. the sabr model is ... |
"local volatility. formulation. local _ volatility > formulation. in mathematical finance, the asset st that underlies a financial derivative is typically assumed to follow a stochastic differential equation of the form d s t = ( r t β d t ) s t d t + Ο t s t d w t { \ displaystyle ds _ { t } = ( r _ { t } - d _ { t } ... |
"local volatility. formulation. local _ volatility > formulation. and when such volatility is merely a function of the current underlying asset level st and of time t, we have a local volatility model. the local volatility model is a useful simplification of the stochastic volatility model." |
"local volatility. formulation. local _ volatility > formulation. "" local volatility "" is thus a term used in quantitative finance to denote the set of diffusion coefficients, Ο t = Ο ( s t, t ) { \ displaystyle \ sigma _ { t } = \ sigma ( s _ { t }, t ) }, that are consistent with market prices for all options on a ... |
"stochastic volatility jump. summary. stochastic _ volatility _ jump. in mathematical finance, the stochastic volatility jump ( svj ) model is suggested by bates. this model fits the observed implied volatility surface well. the model is a heston process for stochastic volatility with an added merton log - normal jump.... |
"no such thing as a free lunch. finance. no _ such _ thing _ as _ a _ free _ lunch > history and usage > meanings > finance. in mathematical finance, the term is also used as an informal synonym for the principle of no - arbitrage. this principle states that a combination of securities that has the same cash - flows as... |
"volatility risk premium. summary. volatility _ risk _ premium. in mathematical finance, the volatility risk premium is a measure of the extra amount investors demand in order to hold a volatile security, above what can be computed based on expected returns. it can be defined as the compensation for inherent volatility... |
"thompson uniqueness theorem. summary. thompson _ uniqueness _ theorem. in mathematical finite group theory, thompson's original uniqueness theorem ( feit & thompson 1963, theorems 24. 5 and 25. 2 ) states that in a minimal simple finite group of odd order there is a unique maximal subgroup containing a given elementar... |
"thompson factorization. summary. thompson _ factorization. in mathematical finite group theory, a thompson factorization, introduced by thompson ( 1966 ), is an expression of some finite groups as a product of two subgroups, usually normalizers or centralizers of p - subgroups for some prime p." |
"aschbacher block. summary. aschbacher _ block. in mathematical finite group theory, a block, sometimes called aschbacher block, is a subgroup giving an obstruction to thompson factorization and pushing up. blocks were introduced by michael aschbacher." |
"groups of gf ( 2 ) type. summary. groups _ of _ gf ( 2 ) _ type. in mathematical finite group theory, a group of gf ( 2 ) - type is a group with an involution centralizer whose generalized fitting subgroup is a group of symplectic type ( gorenstein 1982, definition 1. 45 ). as the name suggests, many of the groups of ... |
"groups of gf ( 2 ) type. summary. groups _ of _ gf ( 2 ) _ type. the groups of each of these 8 types were classified by various authors. they consist mainly of groups of lie type with all roots of the same length over the field with 2 elements, but also include many exceptional cases, including the majority of the spo... |
"group of symplectic type. summary. group _ of _ symplectic _ type. in mathematical finite group theory, a p - group of symplectic type is a p - group such that all characteristic abelian subgroups are cyclic. according to thompson ( 1968, p. 386 ), the p - groups of symplectic type were classified by p. hall in unpubl... |
"quadratic pair. summary. quadratic _ pair. in mathematical finite group theory, a quadratic pair for the odd prime p, introduced by thompson ( 1971 ), is a finite group g together with a quadratic module, a faithful representation m on a vector space over the finite field with p elements such that g is generated by el... |
"rank 3 permutation group. summary. rank _ 3 _ permutation _ group. in mathematical finite group theory, a rank 3 permutation group acts transitively on a set such that the stabilizer of a point has 3 orbits. the study of these groups was started by higman ( 1964, 1971 ). several of the sporadic simple groups were disc... |
"n - group ( finite group theory ). summary. n - group _ ( finite _ group _ theory ). in mathematical finite group theory, an n - group is a group all of whose local subgroups ( that is, the normalizers of nontrivial p - subgroups ) are solvable groups. the non - solvable ones were classified by thompson during his wor... |
"exceptional character. summary. exceptional _ character. in mathematical finite group theory, an exceptional character of a group is a character related in a certain way to a character of a subgroup. they were introduced by suzuki ( 1955, p. 663 ), based on ideas due to brauer in ( brauer & nesbitt 1941 )." |
"baer β suzuki theorem. summary. baer β suzuki _ theorem. in mathematical finite group theory, the baer β suzuki theorem, proved by baer ( 1957 ) and suzuki ( 1965 ), states that if any two elements of a conjugacy class c of a finite group generate a nilpotent subgroup, then all elements of the conjugacy class c are co... |
"brauer β fowler theorem. summary. brauer β fowler _ theorem. in mathematical finite group theory, the brauer β fowler theorem, proved by brauer & fowler ( 1955 ), states that if a group g has even order g > 2 then it has a proper subgroup of order greater than g1 / 3. the technique of the proof is to count involutions... |
"dade isometry. summary. dade _ isometry. in mathematical finite group theory, the dade isometry is an isometry from class function on a subgroup h with support on a subset k of h to class functions on a group g ( collins 1990, 6. 1 ). it was introduced by dade ( 1964 ) as a generalization and simplification of an isom... |
"dempwolff group. summary. dempwolff _ group. in mathematical finite group theory, the dempwolff group is a finite group of order 319979520 = 215 Β· 32 Β· 5 Β· 7 Β· 31, that is the unique nonsplit extension 2 5. g l 5 ( f 2 ) { \ displaystyle 2 ^ { 5 \,. } \ mathrm { gl } _ { 5 } ( \ mathbb { f } _ { 2 } ) } of g l 5 ( f 2... |
"dempwolff group. summary. dempwolff _ group. huppert ( 1967, p. 124 ) showed that any extension of g l n ( f q ) { \ displaystyle \ mathrm { gl } _ { n } ( \ mathbb { f } _ { q } ) } by its natural module f q n { \ displaystyle \ mathbb { f } _ { q } ^ { n } } splits if q > 2 { \ displaystyle q > 2 }, and dempwolff ( ... |
"dempwolff group. summary. dempwolff _ group. g l 3 ( f 2 ) { \ displaystyle 2 ^ { 3 \,. } \ mathrm { gl } _ { 3 } ( \ mathbb { f } _ { 2 } ) } is a maximal subgroup of the chevalley group g 2 ( f 3 ) { \ displaystyle g _ { 2 } ( \ mathbb { f } _ { 3 } ) }. the nonsplit extension 2 4." |
"dempwolff group. summary. dempwolff _ group. g l 4 ( f 2 ) { \ displaystyle 2 ^ { 4 \,. } \ mathrm { gl } _ { 4 } ( \ mathbb { f } _ { 2 } ) } is a maximal subgroup of the sporadic conway group co3. the nonsplit extension 2 5. g l 5 ( f 2 ) { \ displaystyle 2 ^ { 5 \,. } \ mathrm { gl } _ { 5 } ( \ mathbb { f } _ { 2 ... |
"gorenstein β harada theorem. summary. gorenstein β harada _ theorem. in mathematical finite group theory, the gorenstein β harada theorem, proved by gorenstein and harada ( 1973, 1974 ) in a 464 - page paper, classifies the simple finite groups of sectional 2 - rank at most 4. it is part of the classification of finit... |
"l - balance theorem. summary. l - balance _ theorem. in mathematical finite group theory, the l - balance theorem was proved by gorenstein & walter ( 1975 ). the letter l stands for the layer of a group, and "" balance "" refers to the property discussed below." |
"puig subgroup. summary. puig _ subgroup. in mathematical finite group theory, the puig subgroup, introduced by puig ( 1976 ), is a characteristic subgroup of a p - group analogous to the thompson subgroup." |
"thompson order formula. summary. thompson _ order _ formula. in mathematical finite group theory, the thompson order formula, introduced by john griggs thompson ( held 1969, p. 279 ), gives a formula for the order of a finite group in terms of the centralizers of involutions, extending the results of brauer & fowler (... |
"thompson subgroup. summary. thompson _ subgroup. in mathematical finite group theory, the thompson subgroup j ( p ) { \ displaystyle j ( p ) } of a finite p - group p refers to one of several characteristic subgroups of p. john g. thompson ( 1964 ) originally defined j ( p ) { \ displaystyle j ( p ) } to be the subgro... |
"thompson transitivity theorem. summary. thompson _ transitivity _ theorem. in mathematical finite group theory, the thompson transitivity theorem gives conditions under which the centralizer of an abelian subgroup a acts transitively on certain subgroups normalized by a. it originated in the proof of the odd order the... |
"classical involution theorem. summary. classical _ involution _ theorem. in mathematical finite group theory, the classical involution theorem of aschbacher ( 1977a, 1977b, 1980 ) classifies simple groups with a classical involution and satisfying some other conditions, showing that they are mostly groups of lie type ... |
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