I think I should give a ref. for this. Ergodic theory and topological dynamics of group actions on homogeneous spaces, M Bekka & M Mayer, Cambridge University Press, P91. In fact, I don't quite believe this fact.

Another correction: The above is true in case of two parabolic $k$-subgroups containing a common minimal parabolic $k$-subgroup of ...........;

A correction: $(M_1M_2)(k)=M_1(k)M_2(k)$

Dear Zroslav: This theorem only holds for the rational points over an algebraically closed field. It seems not true that $(M_1M_2)(k)=(M_1M_2)(k)$ which is true in some special cases, e.g. two parabolic $k$-subgroups of a connected reductive $k$-group.

Dear Zroslav: Which theorem do you mean in the english edition: Lie groups and algebraic groups.

I am reading Ratner's results on the rigidity theorems and do not know whether the generated there is in group sense or the closure of it.