On Certain Automorphisms of Nilpotent Groups

Abstract

Let G be a group. An automorphism 9 of a group G is pointwise inner if 9(x) is conjugate to x for any x € G. We denote by Autc(G) and C* the group of all central automorphisms and the group of all central automorphisms of G fixing Z(G) elementwise, respectively. In this paper, we introduce a natural generalization of the concept of pointwise inner automorphism. And we find certain necessary and sufficient conditions on the finite p-g roup G such that this subgroup of auto morphisms be equal to Inn(G), G* or Autc(G). Also we give some properties of these automorphisms.