Finite groups as isometry groups
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- by D. Asimov
- Trans. Amer. Math. Soc. 216 (1976), 388-390
- DOI: https://doi.org/10.1090/S0002-9947-1976-0390959-4
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Abstract:
We show that given any finite group G of cardinality $k + 1$, there is a Riemannian sphere ${S^{k - 1}}$ (imbeddable isometrically as a hypersurface in ${{\mathbf {R}}^k}$) such that its full isometry group is isomorphic to G. We also show the existence of a finite metric space of cardinality $k(k + 1)$ whose full isometry group is isomorphic to G.References
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 216 (1976), 388-390
- MSC: Primary 53C20; Secondary 50C25
- DOI: https://doi.org/10.1090/S0002-9947-1976-0390959-4
- MathSciNet review: 0390959