A characterization of totally disconnected compactly ruled groups


A locally compact group G is called compactly ruled if it is a directed union of compact open subgroups. We denote by \({\mathcal {SUB}}\left( G\right) \) the space of closed subgroups of G equipped with the Chabauty topology. In this paper, we show that the subspace \({\mathcal {SUB}}_{\scriptscriptstyle \mathrm {co}}\left( G\right) \) of \({\mathcal {SUB}}\left( G\right) \) consisting of compact open subgroups is dense in \({\mathcal {SUB}}\left( G\right) \) if and only if G is totally disconnected compactly ruled.

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The authors would like to thank the anonymous referee for his/her detailed suggestions that helped in formulating a final version of the paper.

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Correspondence to Hatem Hamrouni.

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Communicating Editor: B Sury

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Hamrouni, H., Jlali, Z. A characterization of totally disconnected compactly ruled groups. Proc Math Sci 131, 6 (2021). https://doi.org/10.1007/s12044-020-00601-8

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  • Totally disconnected locally compact group
  • compactly ruled
  • Chabauty topology

Mathematics Subject Classification

  • 22D05