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Sibirsk. Mat. Zh., 2010, Volume 51, Number 3, Pages 638–648 (Mi smj2114)  

This article is cited in 6 scientific papers (total in 6 papers)

Groups isospectral to the degree 10 alternating group

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. We describe the composition structure of every finite group with the same spectrum as that of the alternating group of degree 10 and not isomorphic to it. This group is isomorphic to the semidirect product of the abelian $\{3,7\}$-group, which contains an element of order 21, by the symmetric group of degree 5.

Keywords: spectrum of a group, isospectral groups, recognition of groups by spectrum, simple group, Frobenius group, alternating group.

Full text: PDF file (337 kB)
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English version:
Siberian Mathematical Journal, 2010, 51:3, 507–514

Bibliographic databases:

Document Type: Article
UDC: 512.542
Received: 17.11.2009

Citation: A. M. Staroletov, “Groups isospectral to the degree 10 alternating group”, Sibirsk. Mat. Zh., 51:3 (2010), 638–648; Siberian Math. J., 51:3 (2010), 507–514

Citation in format AMSBIB
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\by A.~M.~Staroletov
\paper Groups isospectral to the degree~10 alternating group
\jour Sibirsk. Mat. Zh.
\yr 2010
\vol 51
\issue 3
\pages 638--648
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\jour Siberian Math. J.
\yr 2010
\vol 51
\issue 3
\pages 507--514
\crossref{https://doi.org/10.1007/s11202-010-0053-0}
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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, “Sporadic composition factors of finite groups isospectral to simple groups”, Sib. elektron. matem. izv., 8 (2011), 268–272  mathnet
    2. Kondratev A.S., “O konechnykh gruppakh s nebolshim prostym spektrom”, Matematicheskii forum (itogi nauki. yug Rossii), 6 (2012), 56–74  elib
    3. A. S. Kondrat'ev, “Finite groups that have the same prime graph as the group $A_{10}$”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), 99–107  mathnet  crossref  mathscinet  isi  elib
    4. Yu. V. Lytkin, “Groups critical with respect to the spectra of alternating and sporadic groups”, Siberian Math. J., 56:1 (2015), 101–106  mathnet  crossref  mathscinet  isi  elib  elib
    5. V. D. Mazurov, “Neraspoznavaemye po spektru konechnye prostye gruppy i izospektralnye im gruppy”, Vladikavk. matem. zhurn., 17:2 (2015), 47–55  mathnet
    6. A. M. Staroletov, “On recognition of alternating groups by prime graph”, Sib. elektron. matem. izv., 14 (2017), 994–1010  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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