Articles
Published 2008-04-09
Keywords
- free groups,
- orthogonal groups,
- Axiom of Choice.
Copyright (c) 2025 Scientia Series A: Mathematical Sciences
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
Free groups of rotations acting without fixed points on the rational unit sphere. (2008). Scientia Series A: Mathematical Sciences, 16, 109-117. https://revistas.usm.cl/scientia/article/view/115
Abstract
The purpose of this paper is to generalize an example of Sato of a free group of rotations of the Euclidean 3-space whose action on the rational unit sphere is fixed point free. Such groups are of interest, as they can be employed to construct paradoxical decompositions of spheres without assuming the Axiom of Choice.
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