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Algebra Logika, 2008, Volume 47, Number 2, Pages 157–173 (Mi al352)  

This article is cited in 34 scientific papers (total in 34 papers)

Spectra of finite linear and unitary groups

A. A. Buturlakin

Novosibirsk State University

Abstract: The spectrum of a finite group is the set of its element orders. An arithmetic criterion determining whether a given natural number belongs to a spectrum of a given group is furnished for all finite special, projective general, and projective special linear and unitary groups.

Keywords: finite simple group, classical group, spectrum of group, linear group, unitary group.

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English version:
Algebra and Logic, 2008, 47:2, 91–99

Bibliographic databases:

UDC: 512.542
Received: 07.11.2007
Revised: 19.12.2007

Citation: A. A. Buturlakin, “Spectra of finite linear and unitary groups”, Algebra Logika, 47:2 (2008), 157–173; Algebra and Logic, 47:2 (2008), 91–99

Citation in format AMSBIB
\by A.~A.~Buturlakin
\paper Spectra of finite linear and unitary groups
\jour Algebra Logika
\yr 2008
\vol 47
\issue 2
\pages 157--173
\jour Algebra and Logic
\yr 2008
\vol 47
\issue 2
\pages 91--99

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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. 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. 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. A. Buturlakin, “Spectra of finite symplectic and orthogonal groups”, Siberian Adv. Math., 21:3 (2011), 176–210  mathnet  crossref  mathscinet
    6. Akhlaghi Z., Khosravi B., Khatami M., “Characterization by prime graph of $PGL(2,p^k)$ where $p$ and $k>1$ are odd”, Int. J. Algebra Comput., 20:7 (2010), 847–873  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. A. Buturlakin, “Isospectral finite simple groups”, Sib. elektron. matem. izv., 7 (2010), 111–114  mathnet  mathscinet
    8. M. A. Grechkoseeva, “Quasirecognizability of simple unitary groups over fields of even order”, Sib. elektron. matem. izv., 7 (2010), 435–444  mathnet
    9. Akbari M., Kheirabadi M., Moghaddamfar A.R., “Recognition by noncommuting graph of finite simple groups L (4)(q)”, Front Math China, 6:1 (2011), 1–16  crossref  mathscinet  zmath  isi  elib  scopus
    10. Khosravi B., Moradi H., “Quasirecognition by prime graph of finite simple groups L (n) (2) and U (n) (2)”, Acta Math Hungar, 132:1–2 (2011), 140–153  crossref  mathscinet  zmath  isi  elib  scopus
    11. 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
    12. 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
    13. Akbari B., Moghaddamfar A.R., “Recognizing by Order and Degree Pattern of Some Projective Special Linear Groups”, Int. J. Algebr. Comput., 22:6 (2012), 1250051  crossref  mathscinet  zmath  isi  scopus
    14. Akbari M., Moghaddamfar A.R., Rahbariyan S., “A Characterization of Some Finite Simple Groups Through their Orders and Degree Patterns”, Algebr. Colloq., 19:3 (2012), 473–482  crossref  mathscinet  zmath  isi  elib  scopus
    15. Kheirabadi M., Moghaddamfar A.R., “Recognizing Some Finite Simple Groups by Noncommuting Graph”, J. Algebra. Appl., 11:4 (2012), 1250077  crossref  mathscinet  zmath  isi  elib  scopus
    16. 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
    17. 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
    18. 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
    19. Momen Z., Khosravi B., “Groups With the Same Orders of Maximal Abelian Subgroups as a(2)(Q)”, Mon.heft. Math., 174:2 (2014), 285–303  crossref  mathscinet  zmath  isi  scopus
    20. Khosravi B. Khosravi B. Oskouei Hamid Reza Dalili, “on Recognition By Prime Graph of the Projective Special Linear Group Over Gf(3)”, Publ. Inst. Math.-Beograd, 95:109 (2014), 255–266  crossref  mathscinet  zmath  isi  scopus
    21. Huang X., Qu X., “Dependence System and Its Structure”, 2014 Tenth International Conference on Computational Intelligence and Security (Cis), IEEE, 2014, 326–329  crossref  isi  scopus
    22. 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
    23. 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
    24. Vasil'ev A.V., “on Finite Groups Isospectral to Simple Classical Groups”, J. Algebra, 423 (2015), 318–374  crossref  mathscinet  zmath  isi  scopus
    25. 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
    26. A. M. Staroletov, “On recognition of alternating groups by prime graph”, Sib. elektron. matem. izv., 14 (2017), 994–1010  mathnet  crossref
    27. Staroletov A., “On Almost Recognizability By Spectrum of Simple Classical Groups”, Int. J. Group Theory, 6:4 (2017), 7–33  crossref  mathscinet  isi
    28. 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
    29. 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
    30. Akbari B., “Ods-Characterization of Some Low-Dimensional Finite Classical Groups”, Int. Electron. J. Algebr., 24 (2018), 73–90  crossref  zmath  isi  scopus
    31. Yuri V. Lytkin, “On finite groups isospectral to the simple groups $S_4(q)$”, Sib. elektron. matem. izv., 15 (2018), 570–584  mathnet  crossref
    32. A. A. Buturlakin, “Spectra of groups $E_8(q)$”, Algebra and Logic, 57:1 (2018), 1–8  mathnet  crossref  crossref  isi
    33. I. B. Gorshkov, N. V. Maslova, “Finite almost simple groups whose Gruenberg–Kegel graphs coincide with Gruenberg–Kegel graphs of solvable groups”, Algebra and Logic, 57:2 (2018), 115–129  mathnet  crossref  crossref  isi
    34. I. Yu. Mogilnykh, “A note on regular subgroups of the automorphism group of the linear Hadamard code”, Sib. elektron. matem. izv., 15 (2018), 1455–1462  mathnet  crossref
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