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Sib. Èlektron. Mat. Izv., 2014, Volume 11, Pages 921–928 (Mi semr537)  

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

Mathematical logic, algebra and number theory

Unrecognizability by spectrum of finite simple orthogonal groups of dimension nine

M. A. Grechkoseevaab, A. M. Staroletovab

a Sobolev Institute of Mathematics, Ac. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova, 2, 630090, Novosibirsk, Russia

Abstract: The spectrum of a finite group is the set of its elements orders. A group $G$ is said to be unrecognizable by spectrum if there are infinitely many pairwise non-isomorphic finite groups having the same spectrum as $G$. We prove that the simple orthogonal group $O_9(q)$ has the same spectrum as $V\rtimes O_8^-(q)$ where $V$ is the natural 8-dimensional module of the simple orthogonal group $O_8^-(q)$, and in particular $O_9(q)$ is unrecognizable by spectrum. Note that for $q=2$, the result was proved earlier by Mazurov and Moghaddamfar.

Keywords: spectrum, element order, orthogonal group, finite simple group.

Full text: PDF file (527 kB)
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Document Type: Article
UDC: 512.542
MSC: 20D06, 20D60
Received November 28, 2014, published December 5, 2014
Language: English

Citation: M. A. Grechkoseeva, A. M. Staroletov, “Unrecognizability by spectrum of finite simple orthogonal groups of dimension nine”, Sib. Èlektron. Mat. Izv., 11 (2014), 921–928

Citation in format AMSBIB
\Bibitem{GreSta14}
\by M.~A.~Grechkoseeva, A.~M.~Staroletov
\paper Unrecognizability by spectrum of finite simple orthogonal groups of~dimension nine
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 921--928
\mathnet{http://mi.mathnet.ru/semr537}


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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. V. D. Mazurov, “Neraspoznavaemye po spektru konechnye prostye gruppy i izospektralnye im gruppy”, Vladikavk. matem. zhurn., 17:2 (2015), 47–55  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. Yuri V. Lytkin, “On finite groups isospectral to the simple groups $S_4(q)$”, Sib. elektron. matem. izv., 15 (2018), 570–584  mathnet  crossref
    4. 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
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