Elliptic elements in Möbius groups.
type: Item
instance of: scholarly article
title: Elliptic elements in Möbius groups.
zbMATH Open document ID: 1180.20041
author: Shihai Yang
published in: Israel Journal of Mathematics
publication date: 2009-10-02T00:00:00Z
review text: The discreteness of Möbius groups is a fundamental problem which has been discussed by many authors. In 1976, \textit{T. Jørgensen} established a discreteness criterion by using the well-known Jørgensen inequality [Am. J. Math. 98, 739-749 (1976; Zbl 0336.30007)]. This criterion has become standard in the literature. Afterwards many authors tried to generalize it. In this paper, the author, under a restriction on \(\dim(M_G)\), gives the discreteness criterion by the following theorem. Theorem: Let \(G\subset\text{Isom}(H^n)\) be a nonelementary subgroup and \(\dim(M_G)\) be even. If \(G\) contains an elliptic element, then \(G\) is discrete if and only if \(WY(G)\) is discrete and each nonelementary subgroup of \(G\) generated by two elliptic elements is discrete.
reviewed by: Sebahattin Ikikardes
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 30F45
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 5610608
zbMATH Keywords: discreteness criteria
zbMATH Keywords: Möbius groups
zbMATH Keywords: elliptic elements
zbMATH Keywords: Jørgensen inequality
MaRDI profile type: Publication
full work available at URL: s11856-009-0074-1
OpenAlex ID: W1984854180
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DOI: 10.1007/S11856-009-0074-1
description: scientific article; zbMATH DE number 5610608