Almost simple group


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: if it fits between a simple group and its automorphism group. In symbols, a group A is almost simple if there is a simple group S such that

Examples

The full automorphism group of a nonabelian simple group is a complete group, but proper subgroups of the full automorphism group need not be complete.

Structure

By the Schreier conjecture, now generally accepted as a corollary of the classification of finite simple groups, the outer automorphism group of a finite simple group is a solvable group. Thus a finite almost simple group is an extension of a solvable group by a simple group.