×

Topologisch quasinormale Untergruppen zusammenhängender lokalkompakter Gruppen. (English) Zbl 0543.22003

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.

MSC:

22D05 General properties and structure of locally compact groups
57S05 Topological properties of groups of homeomorphisms or diffeomorphisms
22E05 Local Lie groups
57S20 Noncompact Lie groups of transformations
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Bourbaki, N.: Éléments de Mathématique. Groupes et Algèbres de Lie. Chap. I. Paris: Hermann. 1960. · Zbl 0199.35203
[2] Dixmier, J.: L’application exponentielle dans les groupes de Lie résolubles. Bull. Soc. Math. France85, 113-121 (1957). · Zbl 0077.25203
[3] Hochschild, G.: The Structure of Lie Groups. San Francisco-London-Amsterdam: Holden-Day. 1965. · Zbl 0131.02702
[4] Iwasawa, K.: On some types of topological groups. Ann. Math.50, 507-558 (1949). · Zbl 0034.01803 · doi:10.2307/1969548
[5] Kümmich, F., Scheerer, H.: Sottogruppi topologicamente quasi-normali dei gruppi localmente compatti. Rend. Sem. Mat. Univ. Padova69, 195-210 (1983).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.