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If is a Grigorchuk–Gupta–Sidki group defined over a -adic tree, where is an odd prime, we study the existence of Beauville surfaces associated to the quotients of by its level stabilizers . We prove that if is periodic then the quotients are Beauville groups for every if and if . In this case, we further show that all but finitely many quotients of are Beauville groups. On the other hand, if is non-periodic, then none of the quotients are Beauville groups.
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Şükran Gül, Jone Uria-Albizuri, Grigorchuk–Gupta–Sidki groups as a source for Beauville surfaces. Groups Geom. Dyn. 14 (2020), no. 2, pp. 689–704DOI 10.4171/GGD/559