classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26...

of finite simple groups of Lie type does have a precise definition, and they make up most of the groups in the classification of finite simple groups. The...

classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is either...

classification of finite simple groups. Inspection of the list of finite simple groups shows that groups of Lie type over a finite field include all the finite simple...

sporadic finite groups, or just the sporadic groups. A simple group is a group G that does not have any normal subgroups except for the trivial group and G...

arrives at uniquely determined simple groups, by the Jordan–Hölder theorem. The complete classification of finite simple groups, completed in 2004, is a major...

following list in mathematics contains the finite groups of small order up to group isomorphism. For n = 1, 2, … the number of nonisomorphic groups of order...

linear group Group of Lie type Group scheme HN group Janko group Lie group Simple Lie group Linear algebraic group List of finite simple groups Mathieu...

List of simple groups may refer to: List of finite simple groups List of simple Lie groups This disambiguation page lists articles associated with the...

of the surface is the outer automorphism group of its fundamental group. For the outer automorphism groups of all finite simple groups see the list of...

of finite simple groups says that most finite simple groups arise as the group G(k) of k-rational points of a simple algebraic group G over a finite field...

actions of finite groups on vector spaces. The solvable finite 2-transitive groups were classified by Bertram Huppert. The classification of finite simple groups...

new families of finite simple groups. The Ree groups of type 2G2(32n+1) were introduced by Ree (1960), who showed that they are all simple except for the...

all the minimal finite simple groups. The simple N-groups were classified by Thompson (1968, 1970, 1971, 1973, 1974, 1974b) in a series of 6 papers totaling...

also list of finite simple groups. Baby Monster group Conway group Fischer groups Harada–Norton group Held group Higman–Sims group Janko groups Lyons...

landmark work of mathematical exposition. It lists basic information about 93 finite simple groups. The classification of finite simple groups indicates that...

a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups. The list of simple Lie groups can...

extension of { A i } {\displaystyle \{A_{i}\}} by some simple group. The classification of finite simple groups gives us a complete list of finite simple groups;...

rotation group, SO(3, R) SO(8) indefinite orthogonal group unitary group symplectic group list of finite simple groups list of simple Lie groups Representations...

Examples of finite Coxeter groups include the symmetry groups of regular polytopes, and the Weyl groups of simple Lie algebras. Examples of infinite Coxeter...

cyclic groups of prime order. This is equivalent because a finite group has finite composition length, and every simple abelian group is cyclic of prime...

classification of finite simple groups, a thin group is a finite group such that for every odd prime number p, the Sylow p-subgroups of the 2-local subgroups...

understanding the structure of groups and in the classification of finite simple groups. p-groups arise both as subgroups and as quotient groups. As subgroups, for...

multiplier of dihedral 2-groups has order 2. The Schur multipliers of the finite simple groups are given at the list of finite simple groups. The covering...

many finitely generated recursively presented groups. Bernhard Neumann has shown that there are uncountably many non-isomorphic two generator groups. Therefore...

see Kuiper's theorem. List of finite simple groups SL2(R) Representation theory of SL2(R) Representations of classical Lie groups Here rings are assumed...

a finitely generated group equipped with a word metric satisfying certain properties abstracted from classical hyperbolic geometry. The notion of a hyperbolic...

group. Subgroups, quotients, and direct sums of abelian groups are again abelian. The finite simple abelian groups are exactly the cyclic groups of prime...

In group theory, the Tits group 2F4(2)′, named for Jacques Tits (French: [tits]), is a finite simple group of order    17,971,200 = 211 · 33 · 52 · 13...

Symmetric group. As finite symmetric groups are the groups of all permutations of a set with finite elements, and the alternating groups are groups of even...