Jordan-Holder Theorem for profinite groups and applications
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866912270796193792 |
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| author | Bar-On, Tamar Nikolov, Nikolay |
| author_facet | Bar-On, Tamar Nikolov, Nikolay |
| contents | We generalize the notions of composition series and composition factors for profinite groups, and prove a profinite version of the Jordan-Holder Theorem. We apply this to prove a Galois Theorem for infinite prosolvable extensions. In addition, we investigate the connection between the abstract and topological composition factors of a nonstrongly complete profinite group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jordan-Holder Theorem for profinite groups and applications Bar-On, Tamar Nikolov, Nikolay Group Theory We generalize the notions of composition series and composition factors for profinite groups, and prove a profinite version of the Jordan-Holder Theorem. We apply this to prove a Galois Theorem for infinite prosolvable extensions. In addition, we investigate the connection between the abstract and topological composition factors of a nonstrongly complete profinite group. |
| title | Jordan-Holder Theorem for profinite groups and applications |
| topic | Group Theory |
| url | https://arxiv.org/abs/2503.09177 |