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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2009, Volume 6, Pages 457–464 (Mi semr76)  

This article is cited in 22 scientific papers (total in 22 papers)

Research papers

On Thompson's Conjecture

A. V. Vasil'ev

Sobolev Institute of Mathematics, Novosibirsk, Russia
References:
Abstract: For a finite group $G$ denote by $N(G)$ the set of conjugacy class sizes of $G$. In 1980s J. G. Thompson posed the following conjecture: if $L$ is a finite nonabelian simple group, $G$ is a finite group with trivial center and $N(G)=N(L)$, then $L$ and $G$ are isomorphic. Here we prove Thompson's conjecture when $L$ is one of the groups $A_{10}$ and $L_4(4)$. This is the first time when Thompson's conjecture is checked for groups with connected prime graph.
Keywords: finite group, simple group, conjugacy class size, prime graph of a group.
Received January 21, 2009, published November 23, 2009
Bibliographic databases:
Document Type: Article
UDC: 512.542
MSC: 20D60
Language: English
Citation: A. V. Vasil'ev, “On Thompson's Conjecture”, Sib. Èlektron. Mat. Izv., 6 (2009), 457–464
Citation in format AMSBIB
\Bibitem{Vas09}
\by A.~V.~Vasil'ev
\paper On Thompson's Conjecture
\jour Sib. \`Elektron. Mat. Izv.
\yr 2009
\vol 6
\pages 457--464
\mathnet{http://mi.mathnet.ru/semr76}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2586699}
\elib{https://elibrary.ru/item.asp?id=13035596}
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  • https://www.mathnet.ru/eng/semr/v6/p457
  • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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