Class preserving automorphisms of finite p-groups

Abstract

Let G be a finite p-group of order p^n, where p is a prime and n is a natural number. An automorphism α of G is called a class-preserving automorphism of G if for each x∈G, there exists an element g_x∈G such that α(x)=g^(-1) xg. The main result of the thesis provides a neat bound for the order |Aut_c (G)| of the group Aut_c (G) of all class-preserving automorphisms of G.