The involution width of finite simple groups

TL;DR

This paper proves that every non-abelian finite simple group can be expressed as a product of at most four involutions, establishing a sharp bound on their involution width.

Contribution

It establishes a universal upper bound of four on the involution width for all non-abelian finite simple groups, a result previously unknown.

Findings

Involution width of all non-abelian finite simple groups is at most 4

The bound of 4 is sharp, with some groups achieving this maximum

Provides a new understanding of the structure of finite simple groups

Abstract

For a finite group generated by involutions, the involution width is defined to be the minimal $k\in\mathbb{N}$ such that any group element can be written as a product of at most $k$ involutions. We show that the involution width of every non-abelian finite simple group is at most $4$. This result is sharp, as there are families with involution width precisely 4.