# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1902.09083