Grigorchuk-Gupta-Sidki groups as a source for Beauville surfaces

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Gül Erdem Ş., Uria-Albizuri J.

GROUPS GEOMETRY AND DYNAMICS, vol.14, no.2, pp.689-704, 2020 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.4171/ggd/559
  • Journal Name: GROUPS GEOMETRY AND DYNAMICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.689-704
  • Keywords: Finite p-groups, Beauville p-groups, Beauville surfaces, automorphisms of trees, GGS-groups
  • Open Archive Collection: AVESIS Open Access Collection
  • TED University Affiliated: Yes

Abstract

If G is a Grigorchuk-Gupta-Sidki group defined over a p-adic tree, where p is an odd prime, we study the existence of Beauville surfaces associated to the quotients of G by its level stabilizers st(G)((n)). We prove that if G is periodic then the quotients G/ st(G)(n) are Beauville groups for every n >= 2 if p >= and n 3 if p = 3. In this case, we further show that all but finitely many quotients of G are Beauville groups. On the other hand, if G is non-periodic, then none of the quotients G= st(G)(n) are Beauville groups.