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Decomposition of locally compact coset spaces

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posted on 2025-05-09, 02:43 authored by Colin ReidColin Reid
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 πΊπ‘–βˆ’1 and 𝐺𝑖. In the present article, we generalize this series to an analogous decomposition of the coset space πΊβˆ•π» with respect to closed subgroups, where 𝐺 is locally compact and 𝐻 is compactly generated. This time, the irreducible factors are coset spaces πΊπ‘–βˆ•πΊπ‘–βˆ’1 where 𝐺𝑖 is compactly generated and there is no closed subgroup properly between πΊπ‘–βˆ’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.

Funding

ARC

FL170100032

History

Journal title

Journal of the London Mathematical Society

Volume

107

Issue

1

Pagination

407-440

Publisher

Wiley-Blackwell

Language

  • en, English

College/Research Centre

College of Engineering, Science and Environment

School

School of Information and Physical Sciences

Rights statement

Β© 2022 The Authors. Journal of the London Mathematical Society is copyright Β© 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/).

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