On Finite p-Groups Whose IA-Automorphisms Are All Class Preserving

Abstract

Let G be a finite non-abelian p-group, where p is a prime. An automorphism α of G is called a class preserving automorphism if α(x) ∈ x ^G the conjugacy class of x in G, for all x ∈ G. An automorphism α of G is called an IA-automorphism if x ⁻¹α(x) ∈ G′ for each x ∈ G. In this paper, we give necessary and sufficient conditions on finite p-group G of nilpotency class 2 such that every IA-automorphism is class preserving.

Key Words:

• Central automorphisms
• Class preserving automorphisms
• Finite p-groups
• IA-automorphisms

2010 Mathematics Subject Classification:

• 20D45
• 20D15

ACKNOWLEDGMENTS

The author is grateful to the referee for his/her helpful comments.

Notes

Communicated by P. Tiep.