Almost simple group

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Definition

Symbol-free definition

A group is said to be almost simple if it satisfies the following equivalent conditions:

Definition with symbols

A group G is said to be almost simple if it satisfies the following equivalent conditions:

  • There is a simple non-abelian group S such that S \le T \le \operatorname{Aut}(S) for some group T isomorphic to G.
  • There exists a normal subgroup N of G such that N is a simple non-abelian group and C_G(N) is trivial.
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This is a variation of simplicity|Find other variations of simplicity | Read a survey article on varying simplicity

Relation with other properties

Stronger properties

Facts