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arXiv · 2003.05356

Bounding the number of classes of a finite group in terms of a prime

Attila Maróti·Iulian I. Simion
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Abstract

H\'ethelyi and K\"ulshammer showed that the number of conjugacy classes $k(G)$ of any solvable finite group $G$ whose order is divisible by the square of a prime $p$ is at least $(49p+1)/60$. Here an asymptotic generalization of this result is established. It is proved that there exists a constant $c>0$ such that for any finite group $G$ whose order is divisible by the square of a prime $p$ we have $k(G) \geq cp$.

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Attila Maróti, Iulian I. Simion. 2020-03-11. Bounding the number of classes of a finite group in terms of a prime. https://doi.org/10.1515/jgth-2019-0144

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