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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 1, Pages 44–51
(Mi timm1258)
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This article is cited in 8 scientific papers (total in 8 papers)
On Thompson's conjecture for alternating and symmetric groups of degree greater than 1361
I. B. Gorshkov Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Abstract:
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, simple group, alternating group, symmetric group, conjugacy class, Thompson's conjecture.
Citation:
I. B. Gorshkov, “On Thompson's conjecture for alternating and symmetric groups of degree greater than 1361”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 44–51; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 58–65
Linking options:
https://www.mathnet.ru/eng/timm1258 https://www.mathnet.ru/eng/timm/v22/i1/p44
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Abstract page: | 303 | Full-text PDF : | 70 | References: | 73 | First page: | 11 |
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