A new proof of the Nonsolvable Signalizer Functor Theorem

TL;DR

This paper presents a novel proof of McBride's Nonsolvable Signalizer Functor Theorem, which is crucial for the classification of finite simple groups, complementing existing proofs of related theorems.

Contribution

It provides a new and different proof of McBride's Nonsolvable Signalizer Functor Theorem, enhancing the understanding of the Signalizer Functor Method in group theory.

Findings

New proof of McBride's Nonsolvable Signalizer Functor Theorem

Strengthens the theoretical foundation of the Classification of Finite Simple Groups

Offers alternative approaches to key theorems in group theory

Abstract

The Signalizer Functor Method as developed by Gorenstein and Walter played a fundamental role in the first proof of the Classification of the Finite Simple Groups. It plays a similar role in the new proof of the Classification in the Gorenstein-Lyons-Solomon book series. The key results are Glauberman's Solvable Signalizer Functor Theorem and McBride's Nonsolvable Signalizer Functor Theorem. Given their fundamental role, it is desirable to have new and different proofs of them. This is accomplished in {\em A new proof of the Solvable Signalizer Functor Theorem,} P. Flavell, J. Algebra, 398 (2014) 350--363 for Glauberman's Theorem. The purpose of this paper is to give a new proof of McBride's Theorem.