Beauville structures in finite p-groups

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2017-03-15

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Fernandez-Alcober, Gustavo A.
Gul, Sukran

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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.

Subject Keywords

Beauville group, Finite p-groups, Nottingham group

URI

https://hdl.handle.net/11511/66069

Journal

JOURNAL OF ALGEBRA

DOI

https://doi.org/10.1016/j.jalgebra.2016.11.007

Collections

Department of Mathematics, Article

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Citation Formats

G. A. Fernandez-Alcober and S. Gul, “Beauville structures in finite p-groups,” JOURNAL OF ALGEBRA, pp. 1–23, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/66069.