Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-28T07:31:54.177Z Has data issue: false hasContentIssue false
  • English
  • Français

A Group Theoretic Characterization of the 2-Dimensional Spherical Groups

Published online by Cambridge University Press:  20 November 2018

Andy Miller
Andy Miller*
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, OK, USA 73019
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that for a finite group G to be isomorphic to a subgroup of SO(3) (or, equivalently, of PSL(2, C)) it is necessary and sufficient that G satisfies the property that the normalizer of every cyclic subgroup is either cyclic or dihedral.

Keywords

20D9920F3830F4057S30finite groupKleinian groupspherical grouptriangle group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 4 , 01 December 1989 , pp. 459 - 466
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Burnside, W., The Theory of Groups of Finite Order, Cambridge University Press, 1911.Google Scholar
2. Curtis, C. W., Linear Algebra, Springer-Verlag, 1984.Google Scholar
3. Coxeter, H. S. M. and Moser, W. O. J., Generators and Relations for Discrete Groups, Springer- Verlag, 1980.Google Scholar
4. Eilenberg, S., Sur les transformations périodiques de la surface du sphere, Fund. Math. 22 (1934), 28–41.Google Scholar
5. McCullough, D., A. Miller and B. Zimmermann, Group actions on handle bodies, to appear in PTOC. London Math. Soc.Google Scholar
6. McCullough, D., Miller, A. and Zimmermann, B., Group actions on non-closed 2-manifolds, preprint, 1988.Google Scholar
7. Suzuki, M., On a finite group with a partition, Arch. Math. 12 (1961), 241–254.Google Scholar
8. Suzuki, M., Group Theory I, Springer-Verlag, 1982.Google Scholar
9. Weyl, H., Symmetry, Princeton University Press, 1952.Google Scholar
10. Wolf, J. A., Spaces of Constant Curvature, Publish or Perish, 1977.Google Scholar