• COMMUTATOR OF AUTOMORPHISMS

Abstract

In this paper we define the commutator of automorphisms in groups.Let G be any group and 〖 α〗_1 ,α_(2 ),… be automorphisms of G , then the commutator of automorphisms of wight 2, define as follows;

[α_1,α_2]=〖α_1〗^(-1) 〖α_2〗^(-1) α_1 α_2.
In general, the element
[α_1,α_2...,α_(n-1),α_n]=[[α_1,α_2...,α_(n-1)],α_n]

is the left norm commutator of automorphisms of wight n≥2,which is called a simple commutator of automorphisms of wight n.

And in particular we prove some properties of them.