On strongly $p$-embedded subgroups of Lie rank 2

TL;DR

This paper investigates the structure of finite groups with strongly p-embedded subgroups, focusing on cases where the subgroup's generalized Fitting subgroup is a simple Lie rank 2 group in characteristic p.

Contribution

It explores the conditions under which a strongly p-embedded subgroup's F^*(H) is a simple Lie rank 2 group, advancing understanding of subgroup structure in finite groups.

Findings

Identifies conditions for F^*(H) to be a simple Lie rank 2 group

Provides classification results for strongly p-embedded subgroups

Enhances understanding of subgroup embedding in finite groups

Abstract

Suppose that $p$ is a prime, $G$ is a finite group and $H$ is a strongly $p$-embedded subgroup in $G$. We consider the possibility that $F^*(H)$ is a simple group of Lie rank 2 defined in characteristic $p$.