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

2018/03/13 by Şükran Gül, Gül, Şükran, Jone Uria-Albizuri +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1803.04879

arxiv created 2018/03/13 · arxiv updated 2018/03/14

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 \st_G(n). We prove that if G is periodic then the quotients G/\st_G(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/\st_G(n) are Beauville groups.

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