On the parametrized modular group
type: Item
instance of: scholarly article
title: On the parametrized modular group
zbMATH Open document ID: 1343.30036
author: Margarita María Toro
author: Diego Alejandro Mejía
author: Christian Pommerenke
published in: Journal d'Analyse Mathématique
publication date: 2015-11-17T00:00:00Z
review text: The modular group is the most well-known discrete group. In 1936, E. Hecke defined the so-called Hecke groups, which are generalisations of the modular group. Further generalizing the modular group and the Hecke groups, the authors consider the subgroups \(\Pi\) of \(\mathrm{SL}(2,Z[\xi])\) generated by a parabolic element and an elliptic element, where \(Z[\xi]\) is the ring of polynomials of the variable \(\xi\). The elements of \(\Pi\) are classified, and the relators are determined. The authors also investigate the set of all \(\zeta\) for which \(W(\zeta)\) is not loxodromic.
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 6509506
zbMATH Keywords: Hecke groups
zbMATH Keywords: modular group
zbMATH Keywords: parametrized modular group
reviewed by: Ismail Naci Cangül
MaRDI profile type: Publication
full work available at URL: s11854-015-0026-0
OpenAlex ID: W2275580975
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DOI: 10.1007/S11854-015-0026-0
description: scientific article; zbMATH DE number 6509506