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

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, Thompson’s conjecture.

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

Bibliographic databases:

UDC: 512.542
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
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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
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
3. I. B. Gorshkov, “Towards Thompson's conjecture for alternating and symmetric groups”, J. Group Theory, 19:2 (2016), 331–336
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
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
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
7. I. B. Gorshkov, “On Thompson's conjecture for alternating groups of large degree”, J. Group Theory, 20:4 (2017), 719–728
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