Intersection of Solvable Hall subgroups in finite groups

TL;DR

This paper proves that in certain finite groups with a simple classical subgroup, five conjugates of a solvable Hall subgroup intersect trivially, revealing a specific structural property of these groups.

Contribution

It establishes a new result about the intersection properties of solvable Hall subgroups in groups containing simple classical groups.

Findings

Five conjugates of a solvable Hall subgroup intersect trivially.

The result applies to groups containing simple classical groups within automorphism groups.

Provides insight into the subgroup structure of finite groups with classical simple components.

Abstract

In this paper we show that if S is a simple classical group, a group G is contained in inner-diagonal automorphisms of S and contains S, and H is a solvable Hall subgroup of G, then there exists five conjugates of H, whose intersection is trivial.