JournalsggdVol. 14, No. 2pp. 689–704

Grigorchuk–Gupta–Sidki groups as a source for Beauville surfaces

  • Şükran Gül

    TED University, Çankaya/Ankara, Turkey
  • Jone Uria-Albizuri

    BCAM - Basque Center for Applied Mathematics, Bilbao, Spain
Grigorchuk–Gupta–Sidki groups as a source for Beauville surfaces cover
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Abstract

If GG is a Grigorchuk–Gupta–Sidki group defined over a pp-adic tree, where pp is an odd prime, we study the existence of Beauville surfaces associated to the quotients of GG by its level stabilizers stG(n)\mathrm {st}_G(n). We prove that if GG is periodic then the quotients G/stG(n)G/\mathrm {st}_G(n) are Beauville groups for every n2n\geq 2 if p5p\geq 5 and n3n\geq 3 if p=3p = 3. In this case, we further show that all but finitely many quotients of GG are Beauville groups. On the other hand, if GG is non-periodic, then none of the quotients G/stG(n)G/\mathrm {st}_G(n) are Beauville groups.

Cite this article

Şükran Gül, Jone Uria-Albizuri, Grigorchuk–Gupta–Sidki groups as a source for Beauville surfaces. Groups Geom. Dyn. 14 (2020), no. 2, pp. 689–704

DOI 10.4171/GGD/559