Locally compact groups with permutable closed subgroups (Q822694)

A totally disconnected topological group \(G\) is called \textit{periodic} if \(G\) has only compact elements. The authors of this paper intensively study the class of all periodic locally compact groups in their book [\textit{W. Herfort} et al., Periodic locally compact groups. Berlin etc.: de Gruyter (2019; Zbl 1423.22001)]. A locally compact group \(G\) is called \textit{strongly topologically quasihamiltonian} if \(G\) has permutable closed subgroups. (This means: For any two closed subgroups \(X\) and \(Y\) of \(G\) one has \(XY=YX\) and this product is closed.) In section 14 of their book [loc. cit.] the authors describe the class of those groups. Theorem 14.28 of that section is generalized by the main result (Theorem 1.2) of this interesting paper: A classification of all locally compact periodic strongly topologically quasihamiltonian groups is given.