Finite groups as isometry groups
Author: D. Asimov
Journal: Trans. Amer. Math. Soc. 216 (1976), 388-390
MSC: Primary 53C20; Secondary 50C25
MathSciNet review: 0390959
Abstract: We show that given any finite group G of cardinality , there is a Riemannian sphere (imbeddable isometrically as a hypersurface in ) such that its full isometry group is isomorphic to G. We also show the existence of a finite metric space of cardinality whose full isometry group is isomorphic to G.
Keywords: Group, isometry, Riemannian, manifold, the metric space
Article copyright: © Copyright 1976 American Mathematical Society