Semicomplete Finite p-Groups

Abstract

Let G be a group and G' be its commutator subgroup. An automorphism α of G is called an IA-automorphism if x-1α (x) ∈ G' for each x ∈ G. The set of all IA-automorphisms of G is denoted by IA (G). A group G is called semicomplete if and only if IA (G)= Inn (G), where Inn (G) is the inner automorphism group of G. In this paper we characterize semicomplete finite p-groups of class 2, give some necessary conditions for finite p-groups to be semicomplete, and characterize semicomplete non-abelian groups of orders p4 and p5.