Epimorphic subgroups of simple algebraic groups

TL;DR

This paper constructs small epimorphic subgroups within simple algebraic groups over algebraically closed fields, advancing understanding of subgroup structures in algebraic group theory.

Contribution

It introduces a method to explicitly construct epimorphic subgroups of bounded dimension (up to five) in simple algebraic groups over arbitrary characteristic fields.

Findings

Constructed epimorphic subgroups of dimension at most five.

Provided a new approach to subgroup classification in simple algebraic groups.

Extended results to fields of arbitrary characteristic.

Abstract

A morphism of linear algebraic groups $\phi:K\rightarrow G$ is called an epimorphism if it admits right cancellation. A subgroup $H\leq G$ is epimorphic if the inclusion map is an epimorphism. For $G$ a simple algebraic group over an algebraically closed field of arbitrary characteristic we construct epimorphic subgroups of bounded dimension (at most five).