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Sibirsk. Mat. Zh., 2012, Volume 53, Number 3, Pages 663–671 (Mi smj2353)  

This article is cited in 4 scientific papers (total in 4 papers)

On recognition by spectrum of the simple groups $B_3(q)$, $C_3(q)$, and $D_4(q)$

A. M. Staroletov

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

Abstract: The spectrum of a finite group is the set of its element orders. Two groups are isospectral whenever they have the same spectra. We consider the classes of finite groups isospectral to the simple symplectic and orthogonal groups $B_3(q)$, $C_3(q)$, and $D_4(q)$. We prove that in the case of even characteristic and $q>2$ these groups can be reconstructed from their spectra up to isomorphisms. In the case of odd characteristic we obtain a restriction on the composition structure of groups of this class.

Keywords: finite group, simple symplectic and orthogonal groups, spectrum of a group, recognition by spectrum.

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English version:
Siberian Mathematical Journal, 2012, 53:3, 532–538

Bibliographic databases:

UDC: 512.542
Received: 15.06.2011

Citation: A. M. Staroletov, “On recognition by spectrum of the simple groups $B_3(q)$, $C_3(q)$, and $D_4(q)$”, Sibirsk. Mat. Zh., 53:3 (2012), 663–671; Siberian Math. J., 53:3 (2012), 532–538

Citation in format AMSBIB
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\paper On recognition by spectrum of the simple groups $B_3(q)$, $C_3(q)$, and $D_4(q)$
\jour Sibirsk. Mat. Zh.
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\vol 53
\issue 3
\pages 663--671
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\jour Siberian Math. J.
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\vol 53
\issue 3
\pages 532--538
\crossref{https://doi.org/10.1134/S0037446612020334}
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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. 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
    2. 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
    3. 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
    4. 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
  • Сибирский математический журнал Siberian Mathematical Journal
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