Almost simple group

Summary

In mathematics, a group is said to be almost simple if it contains a non-abelian simple group and is contained within the automorphism group of that simple group – that is, if it fits between a (non-abelian) simple group and its automorphism group. In symbols, a group $A$ is almost simple if there is a (non-abelian) simple group S such that $S \leq A \leq \operatorname{Aut}(S)$, where the inclusion of $S$ in $\mathrm{Aut}(S)$ is the action by conjugation, which is faithful since $S$ has a trivial center.