Verification of an old conjecture on nonabelian 2–generated groups of order p3

Abstract

A longstanding conjecture in group theory states: "Every finite non-abelian p-group possesses at least a non-inner automorphism of order p", where p is a prime number. Recently, an updated classification of 2-generated p-groups of nilpotency class two has been published. Using this classification, we prove the verification of this conjecture for 2-generated groups of order p3.