Topologisch quasinormale Untergruppen zusammenhängender lokalkompakter Gruppen (Q795935)

A closed subgroup Q of a topological group G is called topologically quasinormal (tqn) in G if \(\overline{AQ}=\overline{QA}\) holds for every (closed) subgroup A of G. It has been conjectured that every tqn subgroup of a connected locally compact group is actually a normal subgroup. We prove this to be correct, and besides are showing: a homogeneous space G/H of a connected Lie group G with the property that every non-trivial one-parameter orbit is dense has dimension at most one.