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.
On the asymptotic behaviour of the number of Beauville and non-Beauville p-groups / Fernandez Alcober GA; Gul S; Vannacci M. - In: PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6115. - STAMPA. - 120:(2021), pp. 220-241. [10.1112/plms.12295]
On the asymptotic behaviour of the number of Beauville and non-Beauville p-groups
Vannacci M
2021
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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