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

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

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
\Bibitem{Sta12} \by A.~M.~Staroletov \paper On recognition by spectrum of the simple groups $B_3(q)$, $C_3(q)$, and $D_4(q)$ \jour Sibirsk. Mat. Zh. \yr 2012 \vol 53 \issue 3 \pages 663--671 \mathnet{http://mi.mathnet.ru/smj2353} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978582} \transl \jour Siberian Math. J. \yr 2012 \vol 53 \issue 3 \pages 532--538 \crossref{https://doi.org/10.1134/S0037446612020334} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000307396200014} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84863205647} 

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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. 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
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
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
4. Grechkoseeva M.A., “Element Orders in Covers of Finite Simple Groups of Lie Type”, J. Algebra. Appl., 14:4 (2015), 1550056
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