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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 1069–1078 (Mi semr1115)  

Mathematical logic, algebra and number theory

On the maximal tori in finite linear and unitary groups

Andrei V. Zavarnitsine

Sobolev Institute of Mathematics, 4, Koptyug ave., Novosibirsk, 630090, Russia

Abstract: 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.

Keywords: maximal torus, cyclic decomposition.

Funding Agency Grant Number
Siberian Branch of Russian Academy of Sciences I.1.1., project № 0314-2016-0001
This research was supported by the Program of Fundamental Scientific Research of the SB RAS № I.1.1., project № 0314-2016-0001.


DOI: https://doi.org/10.33048/semi.2019.16.074

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Bibliographic databases:

UDC: 512.542.6
MSC: 20E99, 20G40
Received February 27, 2019, published August 7, 2019
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Citation: Andrei V. Zavarnitsine, “On the maximal tori in finite linear and unitary groups”, Sib. Èlektron. Mat. Izv., 16 (2019), 1069–1078

Citation in format AMSBIB
\Bibitem{Zav19}
\by Andrei~V.~Zavarnitsine
\paper On the maximal tori in finite linear and unitary groups
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1069--1078
\mathnet{http://mi.mathnet.ru/semr1115}
\crossref{https://doi.org/10.33048/semi.2019.16.074}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000479063900007}


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