# Almost simple group

## 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 satisfactions |
This is a variation of simplicity|Find other variations of simplicity | Read a survey article on varying simplicity