Semicomplete Finite p-Groups of Class 2

Abstract

Let G be a group and G' be its commutator subgroup. An automorphism α of a group G is called an IA-automorphism if x-1 α(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 completely characterize semicomplete finite p-groups of class 2; we also classify all semicomplete finite p-groups of order pn (n ≤ 5), where p is an odd prime. This completes our work in 2011.