Locally compact strictly convex metric groups are abelian
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914089633054720 |
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| author | Banakh, Taras Mazurenko, Oles |
| author_facet | Banakh, Taras Mazurenko, Oles |
| contents | We show that every locally compact strictly convex metric group is abelian, thus answering one problem posed by the authors in their earlir paper. To prove this theorem we first construct the isomorphic embeddings of the real line into the strictly convex metric group using its geodesic properties and charaterization of the real line as a unique not monothetic one-parametric metrizable topological group. We proceed to show that all compact subgroups in a strictly convex metric group are trivial, which combined with the classical result of Iwasawa completes the proof of the main result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10755 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Locally compact strictly convex metric groups are abelian Banakh, Taras Mazurenko, Oles Group Theory Functional Analysis General Topology 20K45, 46B20, 52A07 We show that every locally compact strictly convex metric group is abelian, thus answering one problem posed by the authors in their earlir paper. To prove this theorem we first construct the isomorphic embeddings of the real line into the strictly convex metric group using its geodesic properties and charaterization of the real line as a unique not monothetic one-parametric metrizable topological group. We proceed to show that all compact subgroups in a strictly convex metric group are trivial, which combined with the classical result of Iwasawa completes the proof of the main result. |
| title | Locally compact strictly convex metric groups are abelian |
| topic | Group Theory Functional Analysis General Topology 20K45, 46B20, 52A07 |
| url | https://arxiv.org/abs/2510.10755 |