Abstract
LetQ be a subgroup of the locally compact groupG. Q is called a topologically quasinormal subgroup ofG, ifQ is closed and\(\overline {QA} = \overline {AQ} \) for each closed subgroupA ofG. We prove: If the compact elements ofG form a proper subgroup, compact topologically quasinormal subgroups ofG are subnormal of defect 2. IfG is connected, compact topologically quasinormal subgroups ofG are normal. IfG/G 0 is compact, connected topologically quasinormal subgroups ofG are normal.
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Kümmich, F. Quasinormalität in topologischen Gruppen. Monatshefte f#x00FC;r Mathematik 87, 241–245 (1979). https://doi.org/10.1007/BF01303078
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DOI: https://doi.org/10.1007/BF01303078