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Apr 5, 2013 at 15:41 comment added G.J. @Burde: Thanks for your comments. Indeed, I reduced my problem to what you see here, by the use of Onishchik's results (from his book). I guess, further conditions here (specially existence of an orbit of codimension one), forces the intersection to be trivial.
Apr 5, 2013 at 13:23 history answered Dietrich Burde CC BY-SA 3.0