Beauville structures in finite p-groups

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Fernandez-Alcober G. A., Gul S.

JOURNAL OF ALGEBRA, vol.474, pp.1-23, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 474
  • Publication Date: 2017
  • Doi Number: 10.1016/j.jalgebra.2016.11.007
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1-23
  • Middle East Technical University Affiliated: Yes


We study the existence of (unmixed) Beauville structures in finite p-groups, where p is a prime. First of all, we extend Catanese's characterisation of abelian Beauville groups to finite p-groups satisfying certain conditions which are much weaker than commutativity. This result applies to all known families of p-groups with a good behaviour with respect to powers: regular p-groups, powerful p-groups and more generally potent p-groups, and (generalised) p-central p-groups. In particular, our characterisation holds for all p-groups of order at most pP, which allows us to determine the exact number of Beauville groups of order p(5), for p >= 5, and of order p(6), for p >= 7. On the other hand, we determine which quotients of the Nottingham group over F-p are Beauville groups, for an odd prime p. As a consequence, we give the first explicit infinite family of Beauville 3-groups, and we show that there are Beauville 3-groups of order 3(n) for every n >= 5. (C) 2016 Elsevier Inc. All rights reserved.