Minimal generation of finite simple groups of Lie type by regular unipotent elements

TL;DR

This paper demonstrates that finite simple groups of Lie type can be generated by a small number of regular unipotent elements, often two or three, simplifying their generation process.

Contribution

It establishes that all finite simple groups of Lie type can be generated by three regular unipotent elements, with some cases requiring only two, advancing understanding of their structure.

Findings

All finite simple groups of Lie type are generated by three regular unipotent elements.

In certain cases, only two regular unipotent elements are needed for generation.

The results simplify the generation process of these groups.

Abstract

We prove that every finite simple group of Lie type $G$ can be generated by three regular unipotent elements. In certain cases we show that two regular unipotents are sufficient to generate $G$.