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arXiv · 2606.29866

Characterization of the alternating and symmetric groups by the order and conjugacy class sizes

Ilya Gorshkov·Andrey V. Vasil'ev
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Abstract

We prove that an arbitrary finite group $G$ having the same order and same set of conjugacy class sizes as an alternating or symmetric group $S$ must be isomorphic to $S$. From this and previously known results it follows that the same holds true for every simple group $S$.

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Ilya Gorshkov, Andrey V. Vasil'ev. 2026-06-29. Characterization of the alternating and symmetric groups by the order and conjugacy class sizes. https://arxiv.org/abs/2606.29866

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