Given a group G, an element x∈ G and automorphism α∈ Aut (G), the nth autocommutator
[x, n α] is defined recursively by [x, α]= x− 1xα and [x, n α]=[[x, n− 1 α], α] for all n> 1. The …

Let $ G $ be a finite group. The automorphism $ sigma $ of a group $ G $ is said to be an
absolute central automorphism, if for all $ xin G $, $ x^{-1} x^{sigma} in L (G) $, where $ L (G) …

Let 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 …

Let G be a finite group. An automorphism α α of G is called an IA IA automorphism if it
induces the identity automorphism on the abelianized group G/G'G/G′. Let IA (G) IA (G) be …

In this paper we give necessary and sufficient conditions on a p-group G for each absolute
central automorphism of G to be elementary abelian. Also we classify the absolute centre of …

Let G be a finite p-group. The automorphism α of a group G is said to be an absolute central
automorphism, if for all x∈ G, x-1 x α∈ L (G), where L (G) is the absolute center of G. In this …

Let x be an element of a group G and α be an automorphism of G. Then for a positive integer
n, the autocommutator [x, n α] is defined inductively by [x, α]= x− 1xα= x− 1α (x) and [x, n+ 1 …

Let G be a group and let L (G) denote the absolute center of G. An automorphism α of G is
called an absolute central automorphism if x− 1 x α∈ L (G) for each x∈ G. An automorphism …

Let G be a finite p-group. Let Var (G) and IA (G) respectively denote the group of all absolute
central and IA-automorphisms of G. We give necessary and sufficient conditions for a finite …

On Equalities of Central Automorphism Group with Various Automorphism Groups |
SpringerLink Skip to main content Advertisement SpringerLink Account Menu Find a journal …