Free product \(\mathbb{Z}_3*\mathbb{Z}_3\) of rotations with rational entries
type: Item
instance of: scholarly article
title: Free product \(\mathbb{Z}_3*\mathbb{Z}_3\) of rotations with rational entries
zbMATH Open document ID: 0998.20043
DOI: 10.1016/S0024-3795(00)00023-9
author: Guoyang Liu
author: Lewis C. Robertson
published in: Linear Algebra and its Applications
publication date: 2002-08-21T00:00:00Z
review text: The existence of free products and free groups in a rotation group is the key step in establishing the Banach-Tarski paradox [see \textit{S. Wagon}, The Banach-Tarski paradox, Cambridge University Press, Cambridge (1985; Zbl 0569.43001)]. The authors develop an approach to construct the free product \(\mathbb{Z}_3*\mathbb{Z}_3\) as a subgroup of the 3-dimensional special orthogonal group over the rational numbers, avoiding transcendental numbers and irrational numbers.
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 1441340
zbMATH Keywords: special orthogonal groups
zbMATH Keywords: free products
MaRDI profile type: Publication
cites work: Images and quotients of SO(3,R): remarks on a theorem of Van der Waerden
cites work: Free subgroups ofS03(Q)
cites work: The Banach-Tarski Paradox
cites work: Q3687182
Recommended article: Q4462592
Recommended article: Q4527169
Recommended article: Q4385555
Recommended article: Q4549543
Recommended article: On free products in \(\text{SO}_3(\mathbb{Q})\).
Recommended article: On free \({\mathbb{Z}_{p}}\) actions on products of spheres
Recommended article: Free involutions on \(S ^{2} \times S ^{3}\)
Recommended article: On The Schützenberger Product of Three Copies of a Free Group
Recommended article: Free $\mathbb {Z}^p$-actions on the three dimensional torus
Recommended article: Free actions on products of spheres: The rational case
description: scientific article; zbMATH DE number 1441340