Krull-Schmidt Theorem for small profinite groups
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913606263635968 |
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| author | Bar-On, Tamar Nikolov, Nikolay |
| author_facet | Bar-On, Tamar Nikolov, Nikolay |
| contents | We prove that every small profinite group can be decomposed into a direct product of indecomposable profinite groups, and that such a decomposition is unique up to order and isomorphisms of the components. We also investigate the cancellation property of some free pro-$\mathcal{C}$ groups, and give a new criterion for a profinite group to be small. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Krull-Schmidt Theorem for small profinite groups Bar-On, Tamar Nikolov, Nikolay Group Theory We prove that every small profinite group can be decomposed into a direct product of indecomposable profinite groups, and that such a decomposition is unique up to order and isomorphisms of the components. We also investigate the cancellation property of some free pro-$\mathcal{C}$ groups, and give a new criterion for a profinite group to be small. |
| title | Krull-Schmidt Theorem for small profinite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2412.07699 |