Geodesic
On Thompson's conjecture for alternating and symmetric groups of degree greater than 1361
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 44-51

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Let $G$ be a finite group $G$, and let $N(G)$ be the set of sizes of its conjugacy classes. It is shown that if $N(G)$ equals $N(\mathrm{Alt}_n)$ or $N(\mathrm{Sym}_n)$, where $n>1361$, then $G$ has a composition factor isomorphic to an alternating group $\mathrm{Alt}_m$ with $m\leq n$ and the half-interval $(m, n]$ contains no primes.
Keywords: finite group, alternating group, symmetric group, Thompson's conjecture.
Mots-clés : simple group, conjugacy class 
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     title = {On {Thompson's} conjecture for alternating and symmetric groups of degree greater than 1361},
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I. B. Gorshkov. On Thompson's conjecture for alternating and symmetric groups of degree greater than 1361. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 44-51. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a4/