Strong reality of finite simple groups

TL;DR

This paper completes the classification of finite simple strongly real groups, showing that each element in such groups can be expressed as a product of two involutions, solving a longstanding problem.

Contribution

It provides a complete classification of finite simple strongly real groups and confirms that every element can be written as a product of two involutions.

Findings

Classification of finite simple strongly real groups is complete.

Strong reality is equivalent to elements being products of two involutions.

Solved Problem 14.82 from the Kourovka notebook.

Abstract

The classification of finite simple strongly real groups is complete. It is easy to see that strong reality for every nonabelian finite simple group is equivalent to the fact that each element can be written as a product of two involutions. We thus obtain a solution to Problem 14.82 from the Kourovka notebook from the classification of finite simple strongly real groups.