Beauville structures for quotients of generalised GGS-groups

Abstract

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 p n -adic trees, for p any prime and n ≥ 2, also admit Beauville structures.