Geodesic
On the maximal tori in finite linear and unitary groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1069-1078.

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To follow up on the results of [1], we propose a computationally efficient explicit cyclic decomposition of the maximal tori in the groups $\operatorname{SL}_n(q)$ and $\operatorname{SU}_n(q)$ 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.
Mots-clés : maximal torus, cyclic decomposition. 
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     title = {On the maximal tori in finite linear and unitary groups},
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Andrei V. Zavarnitsine. On the maximal tori in finite linear and unitary groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1069-1078. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a17/

[1] A. A. Buturlakin, M. A. Grechkoseeva, “The cyclic structure of maximal tori of the finite classical groups”, Algebra and Logic, 46:2 (2007), 73–89 | DOI | MR | Zbl

[2] A. Storjohann, “Near optimal algorithms for computing Smith normal forms of integer matrices”, Proceedings of the 1996 international symposium on symbolic and algebraic computation, ISSAC '96 (Zürich, Switzerland, July 24–26, 1996), ACM Press, New York, NY, 1996, 267–274 | Zbl

[3] A. V. Zavarnitsine, “Recognition of the simple groups $L_3(q)$ by element orders”, J. Group Theory, 7:1 (2004), 81–97 | MR | Zbl