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

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Fernandez-Alcober G. A., Gül Erdem Ş., Vannacci M.

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, vol.120, no.2, pp.220-241, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 120 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1112/plms.12295
  • Journal Name: PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.220-241
  • Keywords: 20D15 (primary), 14J29, 20F69 (secondary), SURFACES
  • TED University Affiliated: Yes

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.