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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Finite groups as isometry groups


Author: D. Asimov
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0390959-4
Keywords: Group, isometry, Riemannian, manifold, the metric space
Article copyright: © Copyright 1976 American Mathematical Society