A simple construction for a class of $p$-groups with all of their automorphisms central

TL;DR

This paper presents a straightforward linear algebra-based method to construct finite p-groups of nilpotence class 2 where every automorphism is central, contributing a new class of examples in group theory.

Contribution

It introduces a simple, linear algebra-based construction for finite p-groups with all automorphisms central, expanding known examples in the field.

Findings

Constructs a new class of p-groups with all automorphisms central

Uses elementary linear algebra for the construction

Provides explicit examples of such groups

Abstract

We exhibit a simple construction, based on elementary linear algebra, for a class of examples of finite $p$-groups of nilpotence class $2$ all of whose automorphisms are central.