Generation of finite simple groups by an involution and an element of prime order

TL;DR

This paper proves that all non-abelian finite simple groups can be generated using just an involution and a prime order element, simplifying understanding of their structure.

Contribution

It establishes a universal generation property for non-abelian finite simple groups with only two elements, one involution and one prime order element.

Findings

Every non-abelian finite simple group is generated by an involution and a prime order element.

The result applies to all such groups, confirming a broad generational pattern.

Simplifies the structural analysis of finite simple groups.

Abstract

We prove that every non-abelian finite simple group is generated by an involution and an element of prime order.