Beauville structures for quotients of generalised GGS-groups

TL;DR

This paper extends the class of groups known to admit Beauville structures by proving that quotients of infinite periodic GGS-groups acting on p^n-adic trees also possess such structures, broadening the understanding of Beauville surfaces.

Contribution

It generalizes previous results by showing that quotients of infinite periodic GGS-groups on p^n-adic trees admit Beauville structures, for any prime p and n ≥ 2.

Findings

Quotients of infinite periodic GGS-groups on p^n-adic trees admit Beauville structures.

Extension of known results from p-adic trees to p^n-adic trees.

Broader class of groups associated with Beauville surfaces.

Abstract

A finite group with a Beauville structure gives rise to a certain compact complex surface called a Beauville surface. G\"{u}l 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 $n\ge 2$, also admit Beauville structures.