Some remarks on the paper of A. Majeed on freeness of the group \(<a^ n,b^ n>\) for some integer n; a,b\(\in SL(2,{\mathbb{C}})\)
type: Item
instance of: scholarly article
title: Some remarks on the paper of A. Majeed on freeness of the group \(<a^ n,b^ n>\) for some integer n; a,b\(\in SL(2,{\mathbb{C}})\)
zbMATH Open document ID: 0631.20035
DOI: 10.1007/BF03323274
published in: Results in Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The author proves the following theorem on groups G generated by two elements A, B of \(SL_ 2({\mathbb{C}})\), which is more general than the result given in the title: Let G be non-elementary and non-elliptic. Then there is a generating pair \(\{\) U,V\(\}\) of G which is Nielsen-equivalent to \(\{\) A,B\(\}\) such that the subgroup generated by \(U^ n\), \(V^ n\) is a discrete free group of rank 2 for some sufficiently large n.
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 4025700
zbMATH Keywords: generating pair
zbMATH Keywords: Nielsen-equivalent
zbMATH Keywords: discrete free group
author: Gerhard Rosenberger
reviewed by: C. Maclachlan
MaRDI profile type: Publication
cites work: Einige Bemerkungen über Untergruppen der \(\mathrm{PSL}(2, \mathbb C)\)
cites work: Q4145882
cites work: Freeness of the group \(\langle a^n,b^n\rangle\) for some integer \(n,a,b\in SL(2,C)\)
cites work: On Triple Planes (III)
cites work: Surfaces and planar discontinuous groups. Revised and expanded transl. from the German by J. Stillwell
full work available at URL: https://doi.org/10.1007/bf03323274
OpenAlex ID: W1965433553
description: scientific article; zbMATH DE number 4025700