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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2009, Volume 6, Pages 457–464
(Mi semr76)
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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
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
Citation:
A. V. Vasil'ev, “On Thompson's Conjecture”, Sib. Èlektron. Mat. Izv., 6 (2009), 457–464
Linking options:
https://www.mathnet.ru/eng/semr76 https://www.mathnet.ru/eng/semr/v6/p457
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Abstract page: | 619 | Full-text PDF : | 208 | References: | 100 |
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