Elements of prime order in the upper central series of a group of prime-power order

TL;DR

This paper studies the presence of elements of prime order within the upper central series of finite p-groups, providing insights into their structural properties.

Contribution

It offers new results on the distribution and characteristics of elements of order p in the upper central series of p-groups.

Findings

Identifies conditions for elements of order p to appear in the upper central series

Provides classifications of p-groups based on element distribution

Enhances understanding of p-group structure related to prime order elements

Abstract

We investigate the occurrence of elements of order $p$ in the upper central series of a finite $p$-group.