Periodic groups saturated with finite simple groups of lie type rank 1

TL;DR

This paper investigates whether periodic groups saturated with finite simple Lie type groups of rank 1 are themselves simple Lie type groups, providing partial answers to a longstanding mathematical question.

Contribution

It offers a partial solution to the question of whether such saturated groups are necessarily simple Lie type groups, focusing on rank 1 cases.

Findings

Partial confirmation for groups saturated with Lie type rank 1

Insights into the structure of periodic groups with bounded Lie rank

Progress towards understanding saturation and simplicity in group theory

Abstract

In the Kourovka notebook the following question is posed 14.101: Is it true that a periodic group saturated with finite simple groups of Lie type whose ranks are bounded in the aggregate, is itself a simple group of Lie type? In this paper we give a partial answer to this question for periodic groups saturated by finite simple groups of Lie type rank 1.