On the number of classes of conjugate Hall subgroups in finite simple groups

TL;DR

This paper determines the number of conjugate pi-Hall subgroups in all finite almost simple groups and completes the classification of pi-Hall subgroups in finite simple groups, correcting previous errors.

Contribution

It provides a complete classification of pi-Hall subgroups in finite simple groups and clarifies the conjugacy properties in almost simple groups.

Findings

Number of conjugate pi-Hall subgroups in all finite almost simple groups identified

Complete classification of pi-Hall subgroups in finite simple groups achieved

Corrections made to previous classifications and results

Abstract

In this paper we find the number of conjugate $\pi$-Hall subgroups in all finite almost simple groups. We also complete the classification of $\pi$-Hall subgroups in finite simple groups and correct some mistakes from our previous paper.