On equality of certain automorphism groups of finite groups

摘要

Let G be a finite group and L(G) denotes the absolute center of G. An automorphism of G is called an autocentral automorphism if x(-1)(x)L(G) for each xG. An automorphism of G is called a central automorphism if x(-1)(x)Z(G) for each xG. An automorphism of G is called an IA-automorphism if"http://www.w3.org/1999/xlink" for each xG. In this paper, we find necessary and sucient 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.