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exp (nW), n any integer. Then N is a discrete subgroup of the central of G, and so (see [ l ] , p. 12) G/N is a Lie group locally topologically isomorphic with G. But the homomorphism G—>G/N carries S3 into S&/N, which is simply isomorphic with Gz/N = G*. This and the corollary to Theorem 1 complete the proof. E. Cartan [5] has shown that the universal covering group of the group of projective transformations of the line is topologically isomorphic in the large with no linear group.

Characteristics of birational transforms in 𝑆ᵣ