Journal of Lie Theory 33 (2023), No. 1, 297--303
Copyright Heldermann Verlag 2023
On Topologically Quasihamiltonian LC-Groups
Wolfgang Herfort
Department of Analysis and Scientific Computing, University of Technology, Vienna, Austria
w.herfort@tuwien.ac.at
[Abstract-pdf]
A topologically quasihamiltonian group $G$ is defined by the property that any two closed subgroups $X$ and $Y$ give rise to a closed subgroup $\overline{XY}=\overline{YX}$. Y.\,N.\,Mukhin employed lattice theoretic arguments for proving that any such group with a connected component not a singleton set must be commutative. We reprove here this fact -- using only standard arguments from topological group theory.
Keywords: Quasihamiltonian locally compact groups, permutable subgroups.
MSC: 22A05, 22A26.
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