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Algebra Logika, 2008, Volume 47, Number 1, Pages 83–93 (Mi al347)  

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

Recognizability of finite simple groups $L_4(2^m)$ and $U_4(2^m)$ by spectrum

V. D. Mazurovab, G. Y. Chenc

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University
c School of Mathematics and Statistics, Southwest University

Abstract: It is proved that finite simple groups $L_4(2^m)$, $m\ge2$, and $U_4(2^m)$, $m\ge2$, are, up to isomorphism, recognized by spectra, i.e., sets of their element orders, in the class of finite groups. As a consequence the question on recognizability by spectrum is settled for all finite simple groups without elements of order 8.

Keywords: finite simple group, spectrum of group.

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English version:
Algebra and Logic, 2008, 47:1, 49–55

Bibliographic databases:

UDC: 512.542
Received: 28.05.2007

Citation: V. D. Mazurov, G. Y. Chen, “Recognizability of finite simple groups $L_4(2^m)$ and $U_4(2^m)$ by spectrum”, Algebra Logika, 47:1 (2008), 83–93; Algebra and Logic, 47:1 (2008), 49–55

Citation in format AMSBIB
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\paper Recognizability of finite simple groups $L_4(2^m)$ and $U_4(2^m)$ by spectrum
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\vol 47
\issue 1
\pages 83--93
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\jour Algebra and Logic
\yr 2008
\vol 47
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\pages 49--55
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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. 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
    2. 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
    3. 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
    4. M. A. Grechkoseeva, “Quasirecognizability of simple unitary groups over fields of even order”, Sib. elektron. matem. izv., 7 (2010), 435–444  mathnet
    5. A. V. Vasil'ev, M. A. Grechkoseeva, A. M. Staroletov, “On finite groups isospectral to simple linear and unitary groups”, Siberian Math. J., 52:1 (2011), 30–40  mathnet  crossref  mathscinet  isi
    6. 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
    7. Nosratpour P. Darafsheh M.R., “Recognition of the Groups l (5)(4) and U (4)(4) by the Prime Graph”, Ukr. Math. J., 64:2 (2012), 238–246  crossref  mathscinet  zmath  isi  elib  scopus
    8. 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
    9. Babai A., Khosravi B., “Groups With the Same Prime Graph as the Simple Group D (N) (5)”, Ukr. Math. J., 66:5 (2014), 666–677  crossref  mathscinet  zmath  isi  scopus
    10. Grechkoseeva M.A., “Element Orders in Covers of Finite Simple Groups of Lie Type”, J. Algebra. Appl., 14:4 (2015), 1550056  crossref  mathscinet  zmath  isi  elib  scopus
    11. Babai A., Khosravi B., “Quasirecognition By Prime Graph of l-N(2(Alpha)) For Some N and Alpha”, Math. Rep., 17:1 (2015), 119–132  mathscinet  zmath  isi
    12. 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
    13. 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
    14. Nosratpour P., Darafsheh M.R., “Characterization of the Group G(2)(5) By the Prime Graph”, Ukr. Math. J., 68:8 (2017), 1308–1313  crossref  mathscinet  isi  scopus
    15. Alavi S.H., Daneshkhah A., Mosaed H.P., “on Quantitative Structure of Small Ree Groups”, Commun. Algebr., 45:9 (2017), 4099–4108  crossref  mathscinet  zmath  isi  scopus
    16. Mohammadzadeh A., Moghaddamfar A.R., “Several Quantitative Characterizations of Some Specific Groups”, Comment. Math. Univ. Carol., 58:1 (2017), 19–34  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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