抄録
An analytic group G is called (CA) if the group of inner automorphisms of G is closed in the Lie group of all (bicontinuous) automorphisms of G. It has been previously proved by this author that each non- (CA) analytic group G can be densely immersed in a (CA) analytic group H, such that the center of G is closed in H. We now show that there is no (CA) analytic group “smaller” than H into which G can be densely immersed, but H, however, is not the “smallest” such (CA) analytic group. Furthermore, we will isolate those properties of H which determine it uniquely up to dimension, diffeomorphism, diffeomorphism together with local isomorphism, and finally isomorphism.
