Geodesic
On Thompson's Conjecture
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 457-464.

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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, conjugacy class size, prime graph of a group.
Mots-clés : simple group 
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A. V. Vasil'ev. On Thompson's Conjecture. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 457-464. http://geodesic.mathdoc.fr/item/SEMR_2009_6_a21/

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