Finite subgroups of simple algebraic groups with irreducible centralizers

TL;DR

This paper classifies all finite subgroups of simple algebraic groups that have irreducible centralizers, providing a comprehensive understanding of their structure and properties.

Contribution

It offers a complete classification of finite subgroups with irreducible centralizers in simple algebraic groups, a problem not previously fully resolved.

Findings

Identified all finite subgroups with irreducible centralizers

Characterized the structure of these centralizers

Provided new insights into the subgroup structure of simple algebraic groups

Abstract

We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup.