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Algebra Logika, 2012, Volume 51, Number 2, Pages 168–192 (Mi al528)  

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

Thompson's conjecture for simple groups with connected prime graph

I. B. Gorshkov


Abstract: We deal with finite simple groups $G$ with the property $\pi(G)\subseteq\{2,3,5,7,11,13,17\}$, where $\pi(G)$ is the set of all prime divisors of the order of the group $G$. The set of all such groups is denoted by $\zeta_{17}$. A conjecture of Thompson in [Unsolved Problems in Group Theory, The Kourovka Notebook, 17th edn., Institute of Mathematics SO RAN, Novosibirsk (2010), Question 12.38] is proved valid for all groups with connected prime graph in $\zeta_{17}$.

Keywords: finite simple group, Thompsons conjecture.

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English version:
Algebra and Logic, 2012, 51:2, 111–127

Bibliographic databases:

UDC: 512.542
Received: 24.08.2011
Revised: 05.12.2011

Citation: I. B. Gorshkov, “Thompson's conjecture for simple groups with connected prime graph”, Algebra Logika, 51:2 (2012), 168–192; Algebra and Logic, 51:2 (2012), 111–127

Citation in format AMSBIB
\Bibitem{Gor12}
\by I.~B.~Gorshkov
\paper Thompson's conjecture for simple groups with connected prime graph
\jour Algebra Logika
\yr 2012
\vol 51
\issue 2
\pages 168--192
\mathnet{http://mi.mathnet.ru/al528}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2986578}
\zmath{https://zbmath.org/?q=an:06115027}
\transl
\jour Algebra and Logic
\yr 2012
\vol 51
\issue 2
\pages 111--127
\crossref{https://doi.org/10.1007/s10469-012-9175-8}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000307243000002}


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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. Liu Sh. Yang Y., “on Thompson'S Conjecture For Alternating Groups a(P+3)”, Sci. World J., 2014, 752598  crossref  isi  scopus
    2. 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
    3. I. B. Gorshkov, “Towards Thompson's conjecture for alternating and symmetric groups”, J. Group Theory, 19:2 (2016), 331–336  crossref  zmath  isi  elib  scopus
    4. N. Ahanjideh, “Thompson's conjecture for finite simple groups of Lie type $B_n$ and $C_n$”, J. Group Theory, 19:4 (2016), 713–733  crossref  mathscinet  zmath  isi  scopus
    5. A. Babai, A. Mahmoudifa, “Thompson's conjecture for the alternating group of degree $2p$ and $2p+1$”, Czech. Math. J., 67:4 (2017), 1049–1058  crossref  mathscinet  zmath  isi  scopus
    6. N. Ahanjideh, “Thompson's conjecture on conjugacy class sizes for the simple group $PSU_n(q)$”, Int. J. Algebr. Comput., 27:6 (2017), 769–792  crossref  mathscinet  zmath  isi  scopus
    7. I. B. Gorshkov, “On Thompson's conjecture for alternating groups of large degree”, J. Group Theory, 20:4 (2017), 719–728  crossref  mathscinet  zmath  isi  scopus
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