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

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 stG(n). We prove that if G is periodic then the quotients G/stG(n) are Beauville groups for every n≥2 if p≥5 and n≥3 if p=3. On the other hand, if G is non-periodic, then none of the quotients G/stG(n) are Beauville groups.