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Mat. Tr., 2010, Volume 13, Number 2, Pages 33–83 (Mi mt199)  

This article is cited in 31 scientific papers (total in 31 papers)

Spectra of finite symplectic and orthogonal groups

A. A. Buturlakin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: The spectrum of a finite group $G$ is the set of the orders of elements of $G$. In the present article, we obtain an arithmetical description of the spectra of finite symplectic and orthogonal groups. In particular, we describe the spectra of finite simple groups in these two classes.

Key words: spectrum of a group, finite group of Lie type, finite simple group.

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English version:
Siberian Advances in Mathematics, 2011, 21:3, 176–210

Bibliographic databases:

UDC: 512.542
Received: 10.11.2009

Citation: A. A. Buturlakin, “Spectra of finite symplectic and orthogonal groups”, Mat. Tr., 13:2 (2010), 33–83; Siberian Adv. Math., 21:3 (2011), 176–210

Citation in format AMSBIB
\by A.~A.~Buturlakin
\paper Spectra of finite symplectic and orthogonal groups
\jour Mat. Tr.
\yr 2010
\vol 13
\issue 2
\pages 33--83
\jour Siberian Adv. Math.
\yr 2011
\vol 21
\issue 3
\pages 176--210

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    This publication is cited in the following articles:
    1. A. M. Staroletov, “On recognition by spectrum of the simple groups $B_3(q)$, $C_3(q)$, and $D_4(q)$”, Siberian Math. J., 53:3 (2012), 532–538  mathnet  crossref  mathscinet  isi
    2. M. A. Grechkoseeva, D. V. Lytkin, “Almost recognizability by spectrum of finite simple linear groups of prime dimension”, Siberian Math. J., 53:4 (2012), 645–655  mathnet  crossref  mathscinet  isi
    3. D. V. Lytkin, “Large element orders and the characteristic of finite simple symplectic groups”, Siberian Math. J., 54:1 (2013), 78–95  mathnet  crossref  mathscinet  isi
    4. Ahanjideh N., Ahanjideh M., “On the Validity of Thompson's Conjecture for Finite Simple Groups”, Commun. Algebr., 41:11 (2013), 4116–4145  crossref  mathscinet  zmath  isi  elib  scopus
    5. Ahanjideh N., “On the Thompson's Conjecture on Conjugacy Classes Sizes”, Int. J. Algebr. Comput., 23:1 (2013), 37–68  crossref  mathscinet  zmath  isi  elib  scopus
    6. M. A. Zvezdina, “Spectra of automorphic extensions of finite simple symplectic and orthogonal groups over fields of characteristic 2”, Sib. elektron. matem. izv., 11 (2014), 823–832  mathnet
    7. A. A. Buturlakin, A. V. Vasil'ev, “On constructive recognition of finite simple groups by element orders”, Algebra and Logic, 53:4 (2014), 349–351  mathnet  crossref  mathscinet  isi
    8. 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
    9. N. V. Maslova, “Finite simple groups that are not spectrum critical”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 211–215  mathnet  crossref  mathscinet  isi  elib
    10. A. V. Vasil'ev, M. A. Grechkoseeva, “Recognition by spectrum for simple classical groups in characteristic $2$”, Siberian Math. J., 56:6 (2015), 1009–1018  mathnet  crossref  crossref  mathscinet  isi  elib
    11. 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  zmath  isi  elib  scopus
    12. Grechkoseeva M.A., “Element Orders in Covers of Finite Simple Groups of Lie Type”, J. Algebra. Appl., 14:4 (2015), 1550056  crossref  zmath  isi  elib  scopus
    13. Vasil'ev A.V., “on Finite Groups Isospectral To Simple Classical Groups”, J. Algebra, 423 (2015), 318–374  crossref  zmath  isi  scopus
    14. Spiga P., “the Maximum Order of the Elements of a Finite Symplectic Group of Even Characteristic”, Commun. Algebr., 43:4 (2015), 1417–1434  crossref  zmath  isi  elib  scopus
    15. M. A. Grechkoseeva, “On spectra of almost simple groups with symplectic or orthogonal socle”, Siberian Math. J., 57:4 (2016), 582–588  mathnet  crossref  crossref  isi  elib  elib
    16. 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
    17. Bou-Rabee Kh., McReynolds D.B., “Characterizing Linear Groups in Terms of Growth Properties”, Mich. Math. J., 65:3 (2016), 599–611  crossref  mathscinet  zmath  isi  scopus
    18. M. A. Grechkoseeva, D. V. Lytkin, “On maximum orders of elements of simple orthogonal groups in characteristic 2”, Sib. elektron. matem. izv., 14 (2017), 405–417  mathnet  crossref
    19. A. M. Staroletov, “On recognition of alternating groups by prime graph”, Sib. elektron. matem. izv., 14 (2017), 994–1010  mathnet  crossref
    20. Staroletov A., “On Almost Recognizability By Spectrum of Simple Classical Groups”, Int. J. Group Theory, 6:4 (2017), 7–33  crossref  mathscinet  isi
    21. 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
    22. Momen Z., Khosravi B., “Quasirecognition of E-6(Q) By the Orders of Maximal Abelian Subgroups”, J. Algebra. Appl., 17:7 (2018), 1850122  crossref  mathscinet  zmath  isi  scopus
    23. Yuri V. Lytkin, “On finite groups isospectral to the simple groups $S_4(q)$”, Sib. elektron. matem. izv., 15 (2018), 570–584  mathnet  crossref
    24. A. A. Buturlakin, “Spectra of groups $E_8(q)$”, Algebra and Logic, 57:1 (2018), 1–8  mathnet  crossref  crossref  isi
    25. 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
    26. Z. Momen, B. Khosravi, “On recognizability of $\operatorname{PSU}_3(q)$ by the orders of maximal abelian subgroups”, Siberian Math. J., 60:1 (2019), 124–139  mathnet  crossref  crossref  isi  elib
    27. Grechkoseeva M.A., Vasil'ev A.V., Zvezdina M.A., “Recognition of Symplectic and Orthogonal Groups of Small Dimensions By Spectrum”, J. Algebra. Appl., 18:12 (2019), 1950230  crossref  mathscinet  zmath  isi  scopus
    28. Buturlakin A.A., Vasil'ev A.V., “the Graph of Atomic Divisors and Recognition of Finite Simple Groups”, J. Algebra, 537 (2019), 478–502  crossref  mathscinet  zmath  isi  scopus
    29. Gorshkov I.B., “on Thompson'S Conjecture For Finite Simple Groups”, Commun. Algebr., 47:12 (2019), 5192–5206  crossref  mathscinet  zmath  isi  scopus
    30. M. A. Grechkoseeva, M. A. Zvezdina, “O raspoznavaemosti po spektru grupp $L_4(q)$$U_4(q)$”, Sib. matem. zhurn., 61:6 (2020), 1300–1330  mathnet  crossref
    31. A. M. Staroletov, “O kompozitsionnykh faktorakh konechnykh grupp, izospektralnykh prostym klassicheskim gruppam”, Sib. matem. zhurn., 62:2 (2021), 422–440  mathnet  crossref
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