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arXiv · 1810.10986

On the asymptotic behaviour of the number of Beauville and non-Beauville $p$-groups

Gustavo A. Fernández-Alcober·Şükran Gül·Matteo Vannacci
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Abstract

We find asymptotic lower bounds for the numbers of both Beauville and non-Beauville $2$-generator finite $p$-groups of a fixed order, which turn out to coincide with the best known asymptotic lower bound for the total number of $2$-generator finite $p$-groups of the same order. This shows that both Beauville and non-Beauville groups are abundant within the family of finite $p$-groups.

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Gustavo A. Fernández-Alcober, Şükran Gül, Matteo Vannacci. 2018-10-25. On the asymptotic behaviour of the number of Beauville and non-Beauville $p$-groups. https://doi.org/10.1112/plms.12295

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