List of finite simple groups information

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...

mathematics, the classification of finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating...

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...

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...

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

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...

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...

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...

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

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...

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...

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

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...

N} with simple factor group G / N {\displaystyle G/N} , all finite groups may be constructed as a series of extensions with finite simple groups. This fact...

prime order is a simple group, which cannot be broken down into smaller groups. In the classification of finite simple groups, one of the three infinite...

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...

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...

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...

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...

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

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

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

automorphism groups, and their representation theory. For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The...

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...

   ≈ 8×1053. The finite simple groups have been completely classified. Every such group belongs to one of 18 countably infinite families or is one of 26 sporadic...

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

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...

complete classification of finite simple groups. Group theory has three main historical sources: number theory, the theory of algebraic equations, and...

classification of finite simple groups. For a prime number p {\displaystyle p} , a Sylow p-subgroup (sometimes p-Sylow subgroup) of a group G {\displaystyle...