A. A. Buturlakin, M. A. Grechkoseeva, “The cyclic structure of maximal tori of the finite classical groups”, Algebra Logika, 46:2 (2007), 129–156; Algebra and Logic, 46:2 (2007), 73

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Algebra i logika, 2007, Volume 46, Number 2, Pages 129–156 (Mi al1)

This article is cited in 62 scientific papers (total in 62 papers)

The cyclic structure of maximal tori of the finite classical groups

A. A. Buturlakin, M. A. Grechkoseeva

Novosibirsk State University

Full-text PDF (307 kB) Citations (62)

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Abstract: Maximal tori of all finite simple classical groups, as well as of special and general projective linear and unitary groups, are treated. For every such torus, its expression as a direct sum of cyclic groups is obtained in an explicit form.

Keywords: finite simple group, classical group, maximal torus, semisimple element, spectrum of a group.

Received: 11.10.2006

English version:
Algebra and Logic, 2007, Volume 46, Issue 2, Pages 73–89
DOI: https://doi.org/10.1007/s10469-007-0009-z

Bibliographic databases:

UDC: 512.542

Language: Russian

Citation: A. A. Buturlakin, M. A. Grechkoseeva, “The cyclic structure of maximal tori of the finite classical groups”, Algebra Logika, 46:2 (2007), 129–156; Algebra and Logic, 46:2 (2007), 73–89

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Linking options:

https://www.mathnet.ru/eng/al1

https://www.mathnet.ru/eng/al/v46/i2/p129

This publication is cited in the following 62 articles:

Zh. Wang, W. Guo, D. V. Lytkina, V. D. Mazurov, “Periodic Groups Saturated with Finite Simple Symplectic Groups”, Algebra Logic, 2025
Anton A. Baykalov, “Base sizes for finite linear groups with solvable stabilisers”, Journal of Group Theory, 2025
Yanjun Liu, Lizhong Wang, Wolfgang Willems, Jiping Zhang, “Brauer's height zero conjecture for two primes holds true”, Math. Ann., 388:2 (2024), 1677
Anton A. Baykalov, “On algebraic normalisers of maximal tori in simple groups of Lie type”, Journal of Group Theory, 2024
Daniela Bubboloni, Pablo Spiga, Thomas Stefan Weigel, Lecture Notes in Mathematics, 2352, Normal 2-Coverings of the Finite Simple Groups and their Generalizations, 2024, 27
Mahah Javed, Joe Parkin, Peter Rowley, Josh Walton, “The maximal Tori of finite exceptional groups of Lie type”, Communications in Algebra, 2024, 1
A. A. Galt, “Structure of normalizers of maximal tori in groups of Lie type”, Siberian Adv. Math., 34:3 (2024), 209–230
A. A. Galt, A. M. Staroletov, “O rasscheplyaemosti normalizatorov maksimalnykh torov v konechnykh gruppakh lieva tipa”, Algebra i logika, 62:1 (2023), 33–58
A. A. Galt, A. M. Staroletov, “Splitting of Normalizers of Maximal Tori in Finite Groups of Lie Type”, Algebra Logic, 62:1 (2023), 22
Alexander Bors, Michael Giudici, Cheryl Praeger, “Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster”, Memoirs of the AMS, 287:1427 (2023)
Timothy C. Burness, Adam R. Thomas, “Normalisers of maximal tori and a conjecture of Vdovin”, Journal of Algebra, 619 (2023), 459
Saul D. Freedman, Andrea Lucchini, Daniele Nemmi, Colva M. Roney-Dougal, “Finite groups satisfying the independence property”, Int. J. Algebra Comput., 33:03 (2023), 509
A. A. Gal't, A. M. Staroletov, “Minimal supplements of maximal tori in their normalizers for the groups $F_4(q)$”, Izv. Math., 86:1 (2022), 126–149
A. A. Galt, A. M. Staroletov, “O rasscheplyaemosti normalizatorov maksimalnykh torov v gruppakh $E_7(q)$ i $E_8(q)$”, Matem. tr., 24:1 (2021), 52–101
A. P. Khramova, N. V. Maslova, V. V. Panshin, A. M. Staroletov, “Characterization of groups $E_6(3)$ and ${^2}E_6(3)$ by Gruenberg–Kegel graph”, Sib. elektron. matem. izv., 18:2 (2021), 1651–1656
Kulshrestha A., Kundu R., Singh A., “Asymptotics of the Powers in Finite Reductive Groups”, J. Group Theory, 2021
Harper S., “Spread of Almost Simple Classical Groups”, Spread of Almost Simple Classical Groups, Lect. Notes Math., Lecture Notes in Mathematics, 2286, Springer International Publishing Ag, 2021, 1–151
Harper S., “The Spread of Almost Simple Classical Groups Preface”: Harper, S, Spread of Almost Simple Classical Groups, Lect. Notes Math., Lecture Notes in Mathematics, 2286, Springer International Publishing Ag, 2021, V+
A. A. Galt, A. M. Staroletov, “On Splitting of the Normalizer of a Maximal Torus in $E_7(q) $ and $E_8(q) $”, Sib. Adv. Math., 31:4 (2021), 244
Scott Harper, Lecture Notes in Mathematics, 2286, The Spread of Almost Simple Classical Groups, 2021, 53

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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