The essential $l$-dimension of finite groups of Lie type, $l \neq 2$

TL;DR

This paper calculates the essential l-dimension for various finite classical Lie type groups at odd primes l, providing key insights into their algebraic complexity and structure.

Contribution

It introduces explicit computations of the essential l-dimension for classical Lie type groups at odd primes l, extending previous understanding of their algebraic properties.

Findings

Explicit formulas for the essential l-dimension of classical Lie type groups.

Determination of the essential l-dimension for simple factors in Jordan-Hölder series.

Enhanced understanding of the algebraic complexity of finite groups of Lie type.

Abstract

In this paper, we compute the essential $l$-dimension of the finite groups of classical Lie type for odd primes $l$ not equal to the defining prime, specifically the general linear groups, the symplectic groups, the orthogonal groups, and the unitary groups, and the simple factors in their Jordan-H\"older series.