A reduction theorem for simple groups with $e(G) = 3$

Richard Lyons and Ronald Solomon

Vol. 336 (2025), No. 1-2, 351–365

DOI: 10.2140/pjm.2025.336.351

Abstract

This paper highlights the use of transfer to analyze an unbalancing configuration in the GLS classification project for finite simple groups. The configuration occurs when $e(G)=3$, $m_{2,p}(G)=m_p(G)=3$ for some odd prime $p$, and a $p$-component of $p$-rank $1$ is responsible for the unbalancing.

In memory of our dear friend, Gary Seitz

Keywords

finite simple groups, classification, even type, $e(G)=3$

Mathematical Subject Classification

Primary: 20D05

Milestones

Received: 30 April 2024

Accepted: 2 February 2025

Published: 26 May 2025