Normalizer property of finite groups with almost simple subgroups

Abstract

In this paper, we prove that all Coleman automorphisms of extension of an almost simple group by an abelian group or a simple group are inner. Using our methods we also show that the Coleman automorphisms of 2-power order of an odd order group by an almost simple group are inner. In particular, these groups have the normalizer property.

Keywords

• almost simple group
• simple group
• coleman automorphism
• q-central automorphism
• normalizer property