Geodesic
Transitive actions have funny rank one
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999) no. 1, pp. 124-129 
Alexandre M. Sokhet. Transitive actions have funny rank one. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999) no. 1, pp. 124-129. http://geodesic.mathdoc.fr/item/JMAG_1999_6_1_a7/
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     author = {Alexandre M. Sokhet},
     title = {Transitive actions have funny rank one},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {124--129},
     year = {1999},
     volume = {6},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1999_6_1_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Here we prove that any transitive action of a locally compact separable group has funny rank one. This fact has been already proved for the special case of a solvable group. Our theorem is proved, primarily, for the Lie group action case, and then we generalize it by using the approximation of topological groups by Lie groups. We obtain as a natural corollary that the discrete spectrum implies funny rank one.