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arXiv · 1502.02978

On Thompson's conjecture for alternating and symmetric groups

Ilya B. Gorshkov
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Abstract

For a finite group $G$ denote by $N(G)$ the set of conjugesy class sizes of $G$. We show that every finite group $G$ with the property $N(G)=N(Alt_n), n>4$ or $N(G)=N(Sym_n), n>22$ is non-solvable.

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Ilya B. Gorshkov. 2015-02-11. On Thompson's conjecture for alternating and symmetric groups. https://arxiv.org/abs/1502.02978

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