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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2504.04184 |
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| _version_ | 1866913778294063104 |
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| author | Yagasaki, Tatsuhiko |
| author_facet | Yagasaki, Tatsuhiko |
| contents | In this note we clarify general properties of the Hausdorff-like metric on the power set ${\cal S}(G)$ of a group $G$ induced from word length norm and obtain some results on quasi-isometries between some subspaces of ${\cal S}(G)$ and ${\cal S}(H)$ for a group epimorphism $f : G \to H$, when ${\cal S}({\rm Ker}\,f)$ is metrically bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04184 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Note on the induced metric on power sets of groups Yagasaki, Tatsuhiko Group Theory Geometric Topology Primary 20F65, Secondary 51F30 In this note we clarify general properties of the Hausdorff-like metric on the power set ${\cal S}(G)$ of a group $G$ induced from word length norm and obtain some results on quasi-isometries between some subspaces of ${\cal S}(G)$ and ${\cal S}(H)$ for a group epimorphism $f : G \to H$, when ${\cal S}({\rm Ker}\,f)$ is metrically bounded. |
| title | Note on the induced metric on power sets of groups |
| topic | Group Theory Geometric Topology Primary 20F65, Secondary 51F30 |
| url | https://arxiv.org/abs/2504.04184 |