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arXiv · 2301.07633

Supersolvability and nilpotency in terms of the commuting probability and the average character degree

Juan Martínez
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Abstract

Let $p$ be a prime and let $G$ be a finite group such that the smallest prime that divides $|G|$ is $p$. We find sharp bounds, depending on $p$, for the commuting probability and the average character degree to guarantee that $G$ is nilpotent or supersolvable.

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Juan Martínez. 2023-01-18. Supersolvability and nilpotency in terms of the commuting probability and the average character degree. https://arxiv.org/abs/2301.07633

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