On equality of certain automorphism groups of finite groups

Abstract

ABSTRACTLet G be a finite group and L(G) denotes the absolute center of G. An automorphism α of G is called an autocentral automorphism if x−1α(x)∈L(G) for each x∈G. An automorphism α of G is called a central automorphism if x−1α(x)∈Z(G) for each x∈G. An automorphism α of G is called an IA-automorphism if for each x∈G. In this paper, we find necessary and sufficient conditions on G such that every autocentral automorphism is inner. Also we characterize finite non-Abelian p-groups for which every central automorphism is IA-automorphism.