Two Generation of Finite Simple Groups

TL;DR

This paper reviews recent progress on the generation properties of finite simple groups, focusing on their presentations and implications for computational group theory.

Contribution

It consolidates known results on two-generation and (2,3)-generation of finite simple groups, highlighting their significance in computational group theory.

Findings

Finite simple groups are often two-generated.

Many finite simple groups are (2,3)-generated.

These generation properties facilitate computational approaches.

Abstract

This expository article revolves around the question to find short presentations of finite simple groups. This subject is one of the most active research areas of group theory in recent times. We bring together several known results on two-generation and $(2,3)$-generation of finite simple groups and how it impacts computational group theory.