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

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 Be...

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Bibliographic Details
Published in:arXiv.org 2018-03
Main Authors: \c{S}ükran Gül, Uria-Albizuri, Jone
Format: Article
Language:English
Subjects:
Quotients
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Summary: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 \(n\geq 2\) if \(p\geq 5\) and \(n\geq 3\) if \(p=3\). On the other hand, if \(G\) is non-periodic, then none of the quotients \(G/\st_G(n)\) are Beauville groups.
ISSN:2331-8422