Year: 1940
Type: article
Abstract: Let R be the group of all rotations of euclidean three-dimensional space E about its origin.We shall take the domain of operation of R to be a euclidean two-sphere 5 with center at the origin.On the space Sj R is transitive.The group R is topological and, considered as a space, is homeomorphic to projective three-space.While studying the action of groups in certain spaces, the following theorem, which, as far as We know, is not in the literature, occurred to us.THEOREM.Let G be any proper subgroup of R. Then G is not transitive on S.
Authors: Deane Montgomery, Leo Zippin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2077411091