Some results of cohomological properties of $p$-group and non-inner automorphism with order $p$ on non-abelian finite $p$-group

TL;DR

This paper explores the cohomological properties of non-abelian finite p-groups and investigates the existence of non-inner automorphisms of order p within these groups.

Contribution

It provides new insights into the structure of automorphisms of finite p-groups, particularly focusing on non-inner automorphisms of order p.

Findings

Non-abelian finite p-groups have non-inner automorphisms of order p.

Cohomological properties influence automorphism structures.

Results contribute to understanding automorphism groups of p-groups.

Abstract

Any non-abelian finite $p$-group has a non-inner automorphism of order $p$.