Abstract
A closed subgroupQ of a topological groupG is called topologically quasinormal (tqn) inG if\(\overline {AQ} = \overline {QA} \) holds for every closed subgroupA ofG. We show that every tqn subgroup of a connected locally compact group is actually a normal subgroup. Besides we prove: a homogeneous spaceG/H of a connected Lie groupG with the property that every non-trivial one-parameter orbit is dense has dimension at most one.
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Scheiderer, C. Topologisch quasinormale Untergruppen zusammenhängender lokalkompakter Gruppen. Monatshefte für Mathematik 98, 75–81 (1984). https://doi.org/10.1007/BF01536910
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DOI: https://doi.org/10.1007/BF01536910