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On Thompson’s conjecture for alternating and symmetric groups of degree greater than 1361

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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(Alt n ) or N(Sym n ), where n > 1361, then G has a composition factor isomorphic to an alternating group Altm with m ≤ n and the interval (m, n] contains no primes.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    I. B. Gorshkov

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  1. I. B. Gorshkov
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Correspondence to I. B. Gorshkov.

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Original Russian Text © I.B.Gorshkov, 2015, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Vol. 22, No. 1.

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Gorshkov, I.B. On Thompson’s conjecture for alternating and symmetric groups of degree greater than 1361. Proc. Steklov Inst. Math. 293 (Suppl 1), 58–65 (2016). https://doi.org/10.1134/S0081543816050060

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  • DOI: https://doi.org/10.1134/S0081543816050060

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