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Sibirsk. Mat. Zh., 2009, Volume 50, Number 6, Pages 1225–1247 (Mi smj2044)  

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

On finite groups isospectral to simple symplectic and orthogonal groups

A. V. Vasil'ev, M. A. Grechkoseeva, V. D. Mazurov

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. Two groups are said to be isospectral if their spectra coincide. We deal with the class of finite groups isospectral to simple and orthogonal groups over a field of an arbitrary positive characteristic $p$. It is known that a group of this class has a unique nonabelian composition factor. We prove that this factor cannot be isomorphic to an alternating or sporadic group. We also consider the case where this factor is isomorphic to a group of Lie type over a field of the same characteristic $p$.

Keywords: finite group, spectrum of a group, simple group, symplectic group, orthogonal group, composition factor.

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English version:
Siberian Mathematical Journal, 2009, 50:6, 965–981

Bibliographic databases:

UDC: 512.542
Received: 04.08.2009

Citation: A. V. Vasil'ev, M. A. Grechkoseeva, V. D. Mazurov, “On finite groups isospectral to simple symplectic and orthogonal groups”, Sibirsk. Mat. Zh., 50:6 (2009), 1225–1247; Siberian Math. J., 50:6 (2009), 965–981

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. 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
    2. 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
    3. A. M. Staroletov, “Sporadic composition factors of finite groups isospectral to simple groups”, Sib. elektron. matem. izv., 8 (2011), 268–272  mathnet
    4. Ghasemabadi M.F., Iranmanesh A., “Quasirecognition by the prime graph of the group $C_n(2)$, where $n\ne 3$ is odd”, Bull. Malays. Math. Sci. Soc. (2), 34:3 (2011), 529–540  mathscinet  zmath  isi
    5. 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
    6. Ghasemabadi M.F. Iranmanesh A., “2-Quasirecognizability of the Simple Groups B-N(P) and C-N(P) by Prime Graph”, Bull. Iran Math. Soc., 38:3 (2012), 647–668  mathscinet  zmath  isi
    7. Shen H. Cao H. Chen G., “Characterization of Automorphism Groups of Sporadic Simple Groups”, Front. Math. China, 7:3 (2012), 513–519  crossref  mathscinet  zmath  isi  elib  scopus
    8. M. A. Grechkoseeva, “Element orders in covers of finite simple groups”, Algebra and Logic, 52:5 (2013), 426–428  mathnet  crossref  mathscinet  isi
    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  mathscinet  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  mathscinet  zmath  isi  elib  scopus
    13. Vasil'ev A.V., “on Finite Groups Isospectral To Simple Classical Groups”, J. Algebra, 423 (2015), 318–374  crossref  mathscinet  zmath  isi  scopus
    14. Staroletov A., “On Almost Recognizability By Spectrum of Simple Classical Groups”, Int. J. Group Theory, 6:4 (2017), 7–33  crossref  mathscinet  isi
    15. Yuri V. Lytkin, “On finite groups isospectral to the simple groups $S_4(q)$”, Sib. elektron. matem. izv., 15 (2018), 570–584  mathnet  crossref
    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
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