- Title
- Decomposition of locally compact coset spaces
- Creator
- Reid, Colin D.
- Relation
- ARC.FL170100032 http://purl.org/au-research/grants/arc/FL170100032
- Relation
- Journal of the London Mathematical Society Vol. 107, Issue 1, p. 407-440
- Publisher Link
- http://dx.doi.org/10.1112/jlms.12688
- Publisher
- Wiley-Blackwell
- Resource Type
- journal article
- Date
- 2023
- Description
- In a previous article of Wesolek and the author, it was shown that a compactly generated locally compact group 𝐺 admits a finite normal series (𝐺𝑖) in which the factors are compact, discrete or irreducible in the sense that no closed normal subgroup of 𝐺 lies properly between 𝐺𝑖−1 and 𝐺𝑖. In the present article, we generalize this series to an analogous decomposition of the coset space 𝐺∕𝐻 with respect to closed subgroups, where 𝐺 is locally compact and 𝐻 is compactly generated. This time, the irreducible factors are coset spaces 𝐺𝑖∕𝐺𝑖−1 where 𝐺𝑖 is compactly generated and there is no closed subgroup properly between 𝐺𝑖−1 and 𝐺𝑖. Such irreducible coset spaces can be thought of as a generalization of primitive actions of compactly generated locally compact groups; we establish some basic properties and discuss some sources of examples.
- Subject
- coset spaces; closed subgroups; compactly generated locally compact group; finite normal series
- Identifier
- http://hdl.handle.net/1959.13/1480247
- Identifier
- uon:50467
- Identifier
- ISSN:0024-6107
- Rights
- © 2022 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
- Language
- eng
- Full Text
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