Let G be a Lie group and let
Aut(G) denote the group of automorphisms of G. If the subgroup Int (G) of
innerautomorphisms of G is closed in Aut (G), then we call G a (CA) group (after
Van Est.). In this note, we investigate (CA) property of certain classes of Lie groups.
The main results are as follows: THEOREM A. Let G be an analytic group and
suppose that there is no compact semisimple normal subgroup of G. If G
contains a closed uniform (CA) subgroup H, then G is (CA). THEOREM B.
If G is an analytic group whose exponential map is surjective, then G is
(CA).
