Noninner Automorphisms of Order p for Finite p-Groups of Coclass 2

TL;DR

This paper proves that all finite p-groups of coclass 2 possess a noninner automorphism of order p that fixes the center elementwise, advancing understanding of automorphism structures in p-groups.

Contribution

It establishes the existence of specific noninner automorphisms of order p in finite p-groups of coclass 2, a previously unresolved problem.

Findings

Finite p-groups of coclass 2 have noninner automorphisms of order p.

These automorphisms leave the center of the group fixed.

The result applies to all such groups, confirming a general property.

Abstract

Every finite $p$-group of coclass 2 has a noninner automorphism of order $p$ leaving the center elementwise fixed.