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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 2, Pages 58–73 (Mi timm223)  

This article is cited in 7 scientific papers (total in 7 papers)

On recognizability by spectrum of finite simple groups of types $B_n$, $C_n$, and $ ^2D_n$ for$n=2^k$

A. V. Vasil'eva, I. B. Gorshkovb, M. A. Grechkoseevaa, A. S. Kondrat'evc, A. M. Staroletovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University
c Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: The spectrum of a finite group is the set of its element orders. A group is said to be recognizable (by spectrum) if it is isomorphic to any finite group that has the same spectrum. A nonabelian simple group is called quasirecognizable if every finite group with the same spectrum possesses a unique nonabelian composition factor, and this factor is isomorphic to the simple group in question. We consider the problem of recognizability and quasi-recognizability for finite simple groups of types $B_n$, $C_n$, and $ ^2D_n$ with $n=2^k$.

Keywords: finite simple group, spectrum of a group, prime graph, recognition by spectrum, orthogonal group, symplectic group

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 267, suppl. 1, S218–S233

Bibliographic databases:

UDC: 512.542
Received: 29.12.2008

Citation: A. V. Vasil'ev, I. B. Gorshkov, M. A. Grechkoseeva, A. S. Kondrat'ev, A. M. Staroletov, “On recognizability by spectrum of finite simple groups of types $B_n$, $C_n$, and $ ^2D_n$ for$n=2^k$”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 58–73; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S218–S233

Citation in format AMSBIB
\Bibitem{VasGorGre09}
\by A.~V.~Vasil'ev, I.~B.~Gorshkov, M.~A.~Grechkoseeva, A.~S.~Kondrat'ev, A.~M.~Staroletov
\paper On recognizability by spectrum of finite simple groups of types $B_n$, $C_n$, and ${}^2D_n$ for$n=2^k$
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 2
\pages 58--73
\mathnet{http://mi.mathnet.ru/timm223}
\elib{http://elibrary.ru/item.asp?id=12878769}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 267
\issue , suppl. 1
\pages S218--S233
\crossref{https://doi.org/10.1134/S0081543809070207}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000274041900020}


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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. A. V. Vasil'ev, M. A. Grechkoseeva, V. D. Mazurov, “On finite groups isospectral to simple symplectic and orthogonal groups”, Siberian Math. J., 50:6 (2009), 965–981  mathnet  crossref  mathscinet  isi  elib  elib
    2. 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
    3. A. S. Kondratev, “O raspoznavaemosti po spektru konechnykh prostykh ortogonalnykh grupp, II”, Vladikavk. matem. zhurn., 11:4 (2009), 32–43  mathnet  elib
    4. Z. Momen, B. Khosravi, “Groups with the same prime graph as the orthogonal group $B_n(3)$”, Siberian Math. J., 54:3 (2013), 487–500  mathnet  crossref  mathscinet  isi
    5. 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
    6. Staroletov A., “On Almost Recognizability By Spectrum of Simple Classical Groups”, Int. J. Group Theory, 6:4 (2017), 7–33  crossref  mathscinet  isi
    7. 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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