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

This article is cited in 36 scientific papers (total in 36 papers)

The cyclic structure of maximal tori of the finite classical groups

A. A. Buturlakin, M. A. Grechkoseeva

Novosibirsk State University

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.

Full text: PDF file (307 kB)
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English version:
Algebra and Logic, 2007, 46:2, 73–89

Bibliographic databases:

UDC: 512.542
Received: 11.10.2006

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. D. Mazurov, G. Y. Chen, “Recognizability of finite simple groups $L_4(2^m)$ and $U_4(2^m)$ by spectrum”, Algebra and Logic, 47:1 (2008), 49–55  mathnet  crossref  mathscinet  zmath  isi
    2. A. A. Buturlakin, “Spectra of finite linear and unitary groups”, Algebra and Logic, 47:2 (2008), 91–99  mathnet  crossref  mathscinet  zmath  isi
    3. M. A. Grechkoseeva, “Recognition by spectrum for finite linear groups over fields of characteristic 2”, Algebra and Logic, 47:4 (2008), 229–241  mathnet  crossref  mathscinet  zmath  isi
    4. Grechkoseeva M.A., Shi W., Vasilev A.V., “Recognition by spectrum for finite simple groups of Lie type”, Front. Math. China, 3:2 (2008), 275–285  crossref  mathscinet  zmath  isi  elib  scopus
    5. V. D. Mazurov, “O raspoznavanii konechnykh prostykh grupp po spektru”, Tr. In-ta matem., 16:1 (2008), 59–63  mathnet
    6. A. V. Zavarnitsine, “Exceptional action of the simple groups $L_4(q)$ in the defining characteristic”, Sib. elektron. matem. izv., 5 (2008), 68–74  mathnet  mathscinet
    7. A. V. Vasil'ev, I. B. Gorshkov, M. A. Grechkoseeva, A. S. Kondrat'ev, A. M. Staroletov, “On recognizability by spectrum of finite simple groups of types $B_n$, $C_n$, and $ ^2D_n$ for$n=2^k$”, Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S218–S233  mathnet  crossref  isi  elib
    8. A. V. Vasil'ev, M. A. Grechkoseeva, V. D. Mazurov, “On finite groups isospectral to simple symplectic and orthogonal groups”, Siberian Math. J., 50:6 (2009), 965–981  mathnet  crossref  mathscinet  isi  elib  elib
    9. A. V. Vasil'ev, M. A. Grechkoseeva, V. D. Mazurov, “Characterization of the finite simple groups by spectrum and order”, Algebra and Logic, 48:6 (2009), 385–409  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    10. A. S. Kondratev, “O raspoznavaemosti po spektru konechnykh prostykh ortogonalnykh grupp, II”, Vladikavk. matem. zhurn., 11:4 (2009), 32–43  mathnet  elib
    11. A. A. Buturlakin, “Spectra of finite symplectic and orthogonal groups”, Siberian Adv. Math., 21:3 (2011), 176–210  mathnet  crossref  mathscinet
    12. A. A. Buturlakin, “Isospectral finite simple groups”, Sib. elektron. matem. izv., 7 (2010), 111–114  mathnet  mathscinet
    13. Grechkoseeva M.A., “On element orders in covers of finite simple classical groups”, J Algebra, 339:1 (2011), 304–319  crossref  mathscinet  zmath  isi  elib  scopus
    14. Grechkoseeva M.A., “On Spectra of Covers of Finite Simple Classical Groups”, Doklady Mathematics, 84:1 (2011), 464–466  crossref  mathscinet  zmath  isi  elib  elib  scopus
    15. A. V. Vasil'ev, A. M. Staroletov, “Recognizability of groups $G_2(q)$ by spectrum”, Algebra and Logic, 52:1 (2013), 1–14  mathnet  crossref  mathscinet  zmath  isi
    16. A. A. Buturlakin, “Spectra of finite simple groups $E_6(q)$ and $^2E_6(q)$”, Algebra and Logic, 52:3 (2013), 188–202  mathnet  crossref  mathscinet  isi
    17. A. A. Gal't, “On the splitting of the normalizer of a maximal torus in symplectic groups”, Izv. Math., 78:3 (2014), 443–458  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. M. A. Grechkoseeva, A. M. Staroletov, “Unrecognizability by spectrum of finite simple orthogonal groups of dimension nine”, Sib. elektron. matem. izv., 11 (2014), 921–928  mathnet
    19. A. V. Vasil'ev, A. M. Staroletov, “Almost recognizability by spectrum of simple exceptional groups of Lie type”, Algebra and Logic, 53:6 (2015), 433–449  mathnet  crossref  mathscinet  isi
    20. A. V. Zavarnitsine, “Structure of the maximal tori in spin groups”, Siberian Math. J., 56:3 (2015), 425–434  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    21. Guest S., Morris J., Praeger Ch.E., Spiga P., “on the Maximum Orders of Elements of Finite Almost Simple Groups and Primitive Permutation Groups”, Trans. Am. Math. Soc., 367:11 (2015), PII S0002-9947(2015)06293-X, 7665–7694  crossref  mathscinet  zmath  isi  scopus
    22. Grechkoseeva M.A. Vasil'ev A.V., “on the Structure of Finite Groups Isospectral To Finite Simple Groups”, J. Group Theory, 18:5 (2015), 741–759  crossref  mathscinet  zmath  isi  elib  scopus
    23. Galt A., “on Splitting of the Normalizer of a Maximal Torus in Linear Groups”, J. Algebra. Appl., 14:7 (2015), 1550114  crossref  mathscinet  zmath  isi  elib  scopus
    24. Burness T.C., Tong-Viet H.P., “Derangements in Primitive Permutation Groups, With An Application To Character Theory”, Q. J. Math., 66:1 (2015), 63–96  crossref  mathscinet  zmath  isi  scopus
    25. Vasil'ev A.V., “on Finite Groups Isospectral To Simple Classical Groups”, J. Algebra, 423 (2015), 318–374  crossref  mathscinet  zmath  isi  scopus
    26. Spiga P., “the Maximum Order of the Elements of a Finite Symplectic Group of Even Characteristic”, Commun. Algebr., 43:4 (2015), 1417–1434  crossref  mathscinet  zmath  isi  elib  scopus
    27. Sajjadi M., Bibak M., Rezaeezadeh G.R., “Characterization of Some Projective Special Linear Groups in Dimension Four By Their Orders and Degree Patterns”, Bull. Iran Math. Soc., 42:1 (2016), 27–36  mathscinet  zmath  isi
    28. A. A. Buturlakin, “Spectra of the finite simple groups $E_7(q)$”, Siberian Math. J., 57:5 (2016), 769–777  mathnet  crossref  crossref  isi  elib  elib
    29. Grechkoseeva M.A. Zvezdina M.A., “on Spectra of Automorphic Extensions of Finite Simple Groups F-4(Q) and D-3(4)(Q)”, J. Algebra. Appl., 15:9 (2016), 1650168  crossref  mathscinet  zmath  isi  scopus
    30. King C.S.H., “Generation of Finite Simple Groups By An Involution and An Element of Prime Order”, J. Algebra, 478 (2017), 153–173  crossref  mathscinet  zmath  isi  scopus
    31. Harper S., “On the Uniform Spread of Almost Simple Symplectic and Orthogonal Groups”, J. Algebra, 490 (2017), 330–371  crossref  mathscinet  zmath  isi  scopus
    32. Grechkoseeva M.A., “On Orders of Elements of Finite Almost Simple Groups With Linear Or Unitary Socle”, J. Group Theory, 20:6 (2017), 1191–1222  crossref  mathscinet  zmath  isi  scopus
    33. Trefethen S., “Non-Abelian Composition Factors of M-Rational Groups”, J. Algebra, 485 (2017), 288–309  crossref  mathscinet  zmath  isi  scopus
    34. Galt A., “On Splitting of the Normalizer of a Maximal Torus in Orthogonal Groups”, J. Algebra. Appl., 16:9 (2017), 1750174  crossref  mathscinet  zmath  isi  scopus
    35. A. A. Buturlakin, “Spectra of groups $E_8(q)$”, Algebra and Logic, 57:1 (2018), 1–8  mathnet  crossref  crossref  isi
    36. M. A. Grechkoseeva, “On spectra of almost simple extensions of even-dimensional orthogonal groups”, Siberian Math. J., 59:4 (2018), 623–640  mathnet  crossref  crossref  isi  elib
  • Алгебра и логика Algebra and Logic
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