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Algebra Logika, 2008, Volume 47, Number 4, Pages 405–427 (Mi al365)  

This article is cited in 16 scientific papers (total in 16 papers)

Recognition by spectrum for finite linear groups over fields of characteristic 2

M. A. Grechkoseeva

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

Abstract: The spectrum of a finite group is the set of its element orders. For every finite simple linear group $L=L_n(2^k)$, where $11\le n\le18$ or $n>24$, we describe finite groups having the same spectrum as $L$, prove that the number of pairwise nonisomorphic groups with this property is finite, and derive an explicit formula for calculating this number.

Keywords: finite simple group, linear group, order of element, spectrum of group, recognition by spectrum.

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English version:
Algebra and Logic, 2008, 47:4, 229–241

Bibliographic databases:

UDC: 512.542
Received: 29.10.2007

Citation: M. A. Grechkoseeva, “Recognition by spectrum for finite linear groups over fields of characteristic 2”, Algebra Logika, 47:4 (2008), 405–427; Algebra and Logic, 47:4 (2008), 229–241

Citation in format AMSBIB
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\paper Recognition by spectrum for finite linear groups over fields of characteristic~2
\jour Algebra Logika
\yr 2008
\vol 47
\issue 4
\pages 405--427
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\jour Algebra and Logic
\yr 2008
\vol 47
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\pages 229--241
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Vasil'ev, M. A. Grechkoseeva, “Recognition by spectrum for finite simple linear groups of small dimensions over fields of characteristic 2”, Algebra and Logic, 47:5 (2008), 314–320  mathnet  crossref  mathscinet  zmath  isi
    2. 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
    3. O. A. Alekseeva, A. S. Kondrat'ev, “On recognizability of some finite simple orthogonal groups by spectrum”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S10–S23  mathnet  crossref  isi  elib
    4. 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
    5. A. S. Kondratev, “O raspoznavaemosti po spektru konechnykh prostykh ortogonalnykh grupp, II”, Vladikavk. matem. zhurn., 11:4 (2009), 32–43  mathnet  elib
    6. M. A. Grechkoseeva, “Quasirecognizability of simple unitary groups over fields of even order”, Sib. elektron. matem. izv., 7 (2010), 435–444  mathnet
    7. M. A. Grechkoseeva, W. J. Shi, “On finite groups isospectral to finite simple unitary groups over fields of characteristic 2”, Sib. elektron. matem. izv., 10 (2013), 31–37  mathnet
    8. 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
    9. 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
    10. Mahmoudifar A., Khosravi B., “on Quasirecognition By Prime Graph of the Simple Groups a(N)(+) (P) and a(N)(-) (P)”, J. Algebra. Appl., 14:1 (2015), 1550006  crossref  mathscinet  zmath  isi  elib  scopus
    11. Moghaddamfar A.R., Rahbariyan S., “Od-Characterization of Some Projective Special Linear Groups Over the Binary Field and Their Automorphism Groups”, Commun. Algebr., 43:6 (2015), 2308–2334  crossref  mathscinet  zmath  isi  elib  scopus
    12. Liu Sh., “Od-Characterization of Some Alternating Groups”, Turk. J. Math., 39:3 (2015), 395–407  crossref  mathscinet  zmath  isi  scopus
    13. 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
    14. M. A. Zvezdina, “Spectra of automorphic extensions of finite simple exceptional groups of Lie type”, Algebra and Logic, 55:5 (2016), 354–366  mathnet  crossref  crossref  isi
    15. 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
    16. 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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