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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 3, Pages 45–60 (Mi timm574)  

This article is cited in 10 scientific papers (total in 10 papers)

On the structure of finite groups isospectral to an alternating group

I. A. Vakula

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: It is proved that every finite group isospectral to an alternating group $A_n$ of degree $n$ greater than 21 has a chief factor isomorphic to an alternating group $A_k$, where $k\le n$ and the half-interval $(k,n]$ contains no primes.

Keywords: finite groups, alternating groups, spectrum of a group, isospectral groups, chief factors.

Full text: PDF file (259 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 272, suppl. 1, S271–S286

Bibliographic databases:

UDC: 512.542.52
Received: 22.03.2010

Citation: I. A. Vakula, “On the structure of finite groups isospectral to an alternating group”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 3, 2010, 45–60; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S271–S286

Citation in format AMSBIB
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\paper On the structure of finite groups isospectral to an alternating group
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\pages 45--60
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\issue , suppl. 1
\pages S271--S286
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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. I. B. Gorshkov, “Thompson's conjecture for simple groups with connected prime graph”, Algebra and Logic, 51:2 (2012), 111–127  mathnet  crossref  mathscinet  zmath  isi
    2. I. B. Gorshkov, “Recognizability of alternating groups by spectrum”, Algebra and Logic, 52:1 (2013), 41–45  mathnet  crossref  mathscinet  zmath  isi
    3. I. B. Gorshkov, “Recognizability of symmetric groups by spectrum”, Algebra and Logic, 53:6 (2015), 450–457  mathnet  crossref  mathscinet  isi
    4. A. Mahmoudifar, B. Khosravi, “On characterization by order and prime graph for alternating groups”, Siberian Math. J., 56:1 (2015), 125–131  mathnet  crossref  mathscinet  isi  elib  elib
    5. I. B. Gorshkov, “On Thompson's conjecture for alternating and symmetric groups of degree greater than 1361”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 58–65  mathnet  crossref  mathscinet  isi  elib
    6. Gorshkov I.B., Grishkov A.N., “On Recognition By Spectrum of Symmetric Groups”, Sib. Electron. Math. Rep., 13 (2016), 111–121  mathnet  crossref  mathscinet  zmath  isi  scopus
    7. Babai A. Mahmoudifa A., “Thompson'S Conjecture For the Alternating Group of Degree 2&Itp&It and 2&Itp&It+1”, Czech. Math. J., 67:4 (2017), 1049–1058  crossref  mathscinet  zmath  isi  scopus
    8. Gorshkov I.B., “On Thompson'S Conjecture For Alternating Groups of Large Degree”, J. Group Theory, 20:4 (2017), 719–728  crossref  mathscinet  zmath  isi  scopus
    9. Gorshkov I., Staroletov A., “On Groups Having the Prime Graph as Alternating and Symmetric Groups”, Commun. Algebr., 47:9 (2019), 3905–3914  crossref  isi
    10. Gorshkov I.B., “Thompson'S Conjecture For Alternating Groups”, Commun. Algebr., 47:1 (2019), 30–36  crossref  isi
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