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Sib. Èlektron. Mat. Izv., 2010, Volume 7, Pages 14–20 (Mi semr224)  

This article is cited in 2 scientific papers (total in 2 papers)

Research papers

Recognition by spectrum for finite simple groups with orders having prime divisors at most 17

I. B. Gorshkov

Novosibirsk State University

Abstract: The spectrum $\omega(G)$ of a group $G$ is the set of its element orders. We write $h(G)$ to denote the number of pairwise non-isomorphic finite groups $H$ with $\omega(H)=\omega(G)$. We say that $G$ is recognizable by spectrum if $h(G)=1$ and that $G$ is a group with solved recognition-by-spectrum problem if $h(G)$ is known. In the paper we prove that the groups $C_3(4)$ and $D_4(4)$ are recognizable by spectrum. It follows from this result that the recognition-by-spectrum problem is solved for all finite simple groups with orders having prime divisors at most $17$.

Keywords: finite group, simple group, spectrum of a group, recognition by spectrum.

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Bibliographic databases:

Document Type: Article
UDC: 512.542
MSC: 20D05
Received October 28, 2009, published January 21, 2010

Citation: I. B. Gorshkov, “Recognition by spectrum for finite simple groups with orders having prime divisors at most 17”, Sib. Èlektron. Mat. Izv., 7 (2010), 14–20

Citation in format AMSBIB
\Bibitem{Gor10}
\by I.~B.~Gorshkov
\paper Recognition by spectrum for finite simple groups with orders having prime divisors at most 17
\jour Sib. \`Elektron. Mat. Izv.
\yr 2010
\vol 7
\pages 14--20
\mathnet{http://mi.mathnet.ru/semr224}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2586671}


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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. 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
    2. M. S. Nirova, “Reberno simmetrichnye grafy s chislom vershin, ne bolshim 100”, Sib. elektron. matem. izv., 10 (2013), 22–30  mathnet
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