Commuting graphs of odd prime order elements in simple groups

TL;DR

This paper investigates the structure of commuting graphs formed by elements of odd prime order in finite simple groups, aiming to understand their properties and implications for algebraic loop structures.

Contribution

It provides new insights into the commuting graphs of odd prime order elements in finite simple groups, with applications to the study of Bruck and Bol loops of exponent 2.

Findings

Characterization of commuting graphs in simple groups

Connections to algebraic loop structures

Foundation for future structural analysis

Abstract

We study the commuting graph on elements of odd prime order in finite simple groups. The results are used in a forthcoming paper describing the structure of Bruck loops and Bol loops of exponent 2.