Automorphisms of K-groups I

TL;DR

This paper initiates a series developing the theory of automorphisms of nonsolvable finite groups, aiming to provide a new proof of a key theorem in the classification of finite simple groups.

Contribution

It introduces a foundational framework for automorphisms of nonsolvable finite groups, leading to a novel proof of McBride's Nonsolvable Signalizer Functor Theorem.

Findings

Framework for automorphisms of nonsolvable finite groups

Progress towards a new proof of McBride's theorem

Foundation for classification of finite simple groups

Abstract

This is the first in a sequence of papers that will develop the theory of automorphisms of nonsolvable finite groups. The sequence will culminate in a new proof of McBride's Nonsolvable Signalizer Functor Theorem, which is one of the fundamental results required for the proof of the Classification of the Finite Simple Groups.