On the non-inner automorphism conjecture of finite $p$-groups

TL;DR

This paper proves that certain finite p-groups of nilpotency class n (p > 2) always have a non-inner automorphism of order p, confirming a long-standing conjecture in specific cases.

Contribution

It settles the non-inner automorphism conjecture for finite p-groups of nilpotency class n under specific conditions, for primes p > 2.

Findings

Confirmed the conjecture for p > 2 under certain conditions

Identified conditions under which non-inner automorphisms of order p exist

Advances understanding of automorphism structure in finite p-groups

Abstract

A long-standing conjecture asserts that every finite non-abelian $p$-group has a non-inner automorphism of order $p$. In this paper, we settle the conjecture for a finite $p$-group ($p >2$) of nilpotency class $n$ with certain conditions.