Non-inner automorphisms of order p in finite p-groups of coclass 3

TL;DR

This paper investigates the existence of non-inner automorphisms of order p in non-abelian finite p-groups of coclass 3, excluding the case where p equals 3, contributing to the understanding of automorphism structures in these groups.

Contribution

It establishes the existence of at least one non-inner automorphism of order p in certain finite p-groups of coclass 3, for primes p not equal to 3.

Findings

Existence of non-inner automorphisms of order p proven for specific p-groups

Results exclude the case p=3, focusing on other primes

Enhances understanding of automorphism groups in finite p-groups

Abstract

In this paper we study the existence of at least one non-inner automorphism of order p of a non-abelian finite p-group of coclass 3, where p is a prime integer such that p is different from 3.