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arXiv · 1607.03727

On Thompson's conjecture for alternating group of large degree

Ilya Gorshkov
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Abstract

For a finite group $G$, let $N(G)$ denote the set of conjugacy class sizes of $G$. We show that if every finite group $G$ with trivial center such that $N(G)$ equals to $N(Alt_n)$, where $n>1361$ and at least one of numbers $n$ or $n-1$ are decomposed into a sum of two primes, then $G\simeq Alt_n$.

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Ilya Gorshkov. 2016-07-13. On Thompson's conjecture for alternating group of large degree. https://arxiv.org/abs/1607.03727

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