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Self-Chabauty-isolated Locally Compact Groups

Conference paper
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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 290)

Abstract

Let G be a locally compact group. We denote by \({\mathcal {SUB}}\left( G\right) \) the space of closed subgroups of G equipped with the Chabauty topology. The group G is called self-Chabauty-isolated if the point G is isolated in \({\mathcal {SUB}}\left( G\right) \). In this paper we are interested in the following question: Give necessary and sufficient conditions for the group G to be a self-Chabauty-isolated.

Keywords

Locally compact group Lie group Pro-Lie group Discrete subgroup Chabauty topology Frattini subgroup 

1991 Mathematics Subject Classification

22D05 54B20 22E40 

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Sciences at SfaxSfax UniversitySfaxTunisia

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