Algebraic groups generated by semisimple elements

TL;DR

This paper characterizes the subgroup generated by all semisimple elements in a connected linear algebraic group, providing insights into its structure and properties.

Contribution

It offers a new description of the subgroup generated by semisimple elements in connected linear algebraic groups, advancing understanding of their algebraic structure.

Findings

The subgroup generated by semisimple elements is explicitly described.

Structural properties of this subgroup are analyzed.

Results contribute to the theory of algebraic groups.

Abstract

Given a connected linear algebraic group $G$, we descrive the subgroup of $G$ generated by all semisimple elements.