A new proof of the Nonsolvable Signalizer Functor Theorem

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.