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arXiv · 2606.22244

On {2,3,5}-groups with conjugacy classes of distinct sizes

Wei Zhou·Ilya Gorshkov
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Abstract

A finite group G is called an ah-group if any two distinct conjugacy classes of G have distinct sizes. In this paper, we show that if G is an ah-group and \pi(G) \subseteq {2,3,5}, where \pi(G) denotes the set of prime divisors of |G|, then G \cong S_3.

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Wei Zhou, Ilya Gorshkov. 2026-06-20. On {2,3,5}-groups with conjugacy classes of distinct sizes. https://arxiv.org/abs/2606.22244

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