Commuting involutions and elementary abelian subgroups of simple groups

TL;DR

This paper proves that in finite quasi-simple groups, there exists an elementary abelian subgroup intersecting all conjugacy classes of involutions, motivated by questions in representation theory.

Contribution

It establishes the existence of a universal elementary abelian subgroup intersecting all involution classes in finite quasi-simple groups, a novel result in group theory.

Findings

Existence of such subgroups in all finite quasi-simple groups

Implications for representation theory and group structure

Advances understanding of involution conjugacy classes

Abstract

Motivated in part by representation theoretic questions, we prove that if G is a finite quasi-simple group, then there exists an elementary abelian subgroup of G that intersects every conjugacy class of involutions of G.