Classification of groups of central type of order $p^4$

TL;DR

This paper classifies all groups of central type of order p^4, providing a complete understanding of these specific non-abelian groups, which are less understood compared to abelian cases.

Contribution

It offers the first complete classification of non-abelian groups of central type of order p^4, expanding the understanding of these solvable groups.

Findings

All groups of central type of order p^4 are classified.

The classification distinguishes between abelian and non-abelian cases.

Results contribute to the broader understanding of group structures of order p^4.

Abstract

The classification of abelian groups of central type is well known. However, the description of non-abelian groups of central type which are known to be solvable, is far from being understood. In this paper we classify all groups of central type of order $p^4$ where $p$ is a prime number.