The constructive membership problem for discrete two-generator subgroups of \(\operatorname{SL}_2(\mathbb{R})\)
type: Item
instance of: scholarly article
title: The constructive membership problem for discrete two-generator subgroups of \(\operatorname{SL}_2(\mathbb{R})\)
zbMATH Open document ID: 1380.20053
author: Markus Kirschmer
author: Marion G. Rüther
published in: Journal of Algebra
publication date: 2017-05-02T00:00:00Z
review text: Let \(G=\left\langle A,B\right\rangle \) be a discrete two generator subgroup of SL\(_{2}(\mathbb{R})\), where \(A,B\in \) SL\(_{2}(\mathbb{R})\). The constructive membership problem for \(G\) asks whether any given \(M\in \) SL\(_{2}(\mathbb{R})\) lies in \( G\) and if so, how to express \(M\) as a word in the generators \(A\) and \(B\). In the paper under review, the authors solve the constructive membership problem for all discrete two-generator subgroups of SL\(_{2}(\mathbb{R})\).
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 6710539
zbMATH Keywords: constructive membership problem
zbMATH Keywords: Fuchsian group
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2017.02.029
OpenAlex ID: W2599710809
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DOI: 10.1016/J.JALGEBRA.2017.02.029
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description: scientific article; zbMATH DE number 6710539