On the maximal tori in finite linear and unitary groups

TL;DR

This paper presents an efficient method for explicitly decomposing maximal tori in finite linear and unitary groups, simplifying their computation and extending previous results with a generic cyclic decomposition approach.

Contribution

It introduces a new explicit cyclic decomposition method for maximal tori in $SL_n(q)$ and $SU_n(q)$, enhancing computational efficiency and practical applicability.

Findings

Provides a computationally efficient cyclic decomposition algorithm

Simplifies practical calculation of maximal tori

Extends previous theoretical results with a generic cyclic decomposition

Abstract

To follow up on the results of [1], we propose a computationally efficient explicit cyclic decomposition of the maximal tori in the groups $SL_n(q)$ and $SU_n(q)$ and their projective images. We also derive some corollaries to simplify practical calculation of the maximal tori. The result is based on a generic cyclic decomposition of a finite abelian group which might also be of interest.