The essential p-dimension of the split finite quasi-simple groups of classical Lie type

TL;DR

This paper calculates the essential p-dimension for split finite quasi-simple classical Lie type groups at the defining prime, focusing on groups from general linear, symplectic, and orthogonal types.

Contribution

It provides explicit computations of the essential p-dimension for these classical groups, a key invariant in algebraic group theory.

Findings

Essential p-dimension values for classical Lie type groups are determined.

Results apply to groups from general linear, symplectic, and orthogonal families.

Advances understanding of algebraic group invariants at the defining prime.

Abstract

In this paper, we compute the essential $p$-dimension of the split finite quasi-simple groups of classical Lie type at the defining prime, specifically the quasi-simple groups arising from the general linear and special linear groups, the symplectic groups, and the orthogonal groups.