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 orderâ€, where 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.