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arXiv · 1607.06456

Bounds on the number of conjugacy classes of the symmetric and alternating groups

Bret Benesh·Cong Tuan Son Van
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Abstract

Let $G$ be a finite group with Sylow subgroups $P_1,\ldots,P_n$, and let $k(G)$ denote the number of conjugacy classes of $G$. Pyber asked if $k(G) \leq \prod_{i=1}^n k(P_i)$ for all finite groups $G$. With the help of GAP, we prove that Pyber's inequality holds for all symmetric and alternating groups.

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Bret Benesh, Cong Tuan Son Van. 2016-07-21. Bounds on the number of conjugacy classes of the symmetric and alternating groups. https://arxiv.org/abs/1607.06456

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