Dense subgroups of Lie groups. II

Abstract:

Let G be a dense analytic subgroup of an analytic group L. Then G contains a maximal (CA) closed normal analytic suhgroup M and a closed abelian subgroup $A = Z(G) \times E$, where E is a closed vector subgroup of G, such that $G = M \cdot A$, $M \cap A = Z(G)$, $\overline M = M \cdot \overline {Z(G)}$, and $L = M \cdot \overline A$. We also indicate the extent to which a (CA) analytic group is uniquely determined by its center and a dense analytic subgroup.