On finite groups with elements of prime power orders

TL;DR

This paper classifies finite groups where every element has prime power order, covering solvable, non-solvable, and simple cases, and provides detailed results that extend previous work by G. Higman.

Contribution

It offers a comprehensive classification of EPPO-groups, including solvable, non-solvable, and simple groups, expanding the understanding of their structure.

Findings

Classification of solvable EPPO-groups detailed in Theorem 2.4

Extension of G. Higman's results on prime power order elements

Identification of simple EPPO-groups

Abstract

In this paper we study the finite groups in which every element has prime power order, briefly them EPPO-groups. The classification of EPPO-groups is given including the cases of solvable, non-solvable and simple EPPO-groups. This paper is published in Journal of Yunnan Education College, no.1(1986), p.2-10 (in Chinese). Translate it to English is helpful for readers for citing some conclusions of this paper. For example, the result of solvable EPPO-groups(see Theorem 2.4 in the text) is detailed more than G. Higman's conclusion (see reference 1 in this paper).