Some simplifications in the proof of the Sims conjecture

TL;DR

This paper simplifies the proof of the Sims conjecture for almost simple groups by introducing an elementary lemma related to primitive amalgams, making the proof more accessible and streamlined.

Contribution

It provides a new elementary lemma that significantly simplifies the proof of the Sims conjecture for a specific class of groups.

Findings

Simplified proof of the Sims conjecture for almost simple groups

Introduction of an elementary lemma on primitive amalgams

Enhanced understanding of group structure in this context

Abstract

We prove an elementary lemma concerning primitive amalgams and use it to greatly simplify the proof of the Sims conjecture in the case of almost simple groups.