Beauville Structures for Quotients of Generalised GGS-groups

Di Domenico E., Gül Erdem Ş., Thillaisundaram A.

Advances in Group Theory and Applications, vol.18, pp.3-40, 2024 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 18
  • Publication Date: 2024
  • Doi Number: 10.32037/agta-2024-001
  • Journal Name: Advances in Group Theory and Applications
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.3-40
  • Keywords: Beauville structure, finite p-group, groups acting on rooted trees
  • TED University Affiliated: Yes


A finite group with a Beauville structure gives rise to a certain compact complex surface called a Beauville surface. Gül and Uria-Albizuri showed that quotients of the periodic Grigorchuk–Gupta–Sidki (GGS-)groups that act on the p-adic tree, for p an odd prime, admit Beauville structures. We extend their result by showing that quotients of infinite periodic GGS-groups acting on pn-adic trees, for p any prime and n ≥ 2, also admit Beauville structures.