On noninner automorphisms of 2-generator finite p-groups

ABSTRACT

A longstanding conjecture asserts that every finite nonabelian p-group admits a noninner automorphism of order p. In this paper we give some necessary conditions for a possible counterexample G to this conjecture, in the case when G is a 2-generator finite p-group. Then we show that every 2-generator finite p-group with abelian Frattini subgroup has a noninner automorphism of order p.

KEYWORDS:

• p-group
• noninner automorphism

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D45
• 20D15

Acknowledgments

The authors are grateful to the referee for his/her helpful comments on the first draft of the manuscript.