Finite simple groups of small essential dimension

TL;DR

This paper explores the essential dimension of finite groups, linking it to algebraic geometry, and provides a partial classification of simple finite groups with low essential dimension.

Contribution

It introduces the concept of essential dimension for finite groups and offers a partial classification of simple groups with essential dimension ≤ 3.

Findings

Classification of simple finite groups with essential dimension ≤ 3

Connection between essential dimension and birational algebraic geometry

Insights into the structure of finite groups based on essential dimension

Abstract

We discuss the notion of essential dimension of a finite group and explain its relation with birational algebraic geometry. We show how this leads to a (partial) classification of simple finite groups of essential dimension less than or equal to 3.