On S-Split p-Hilbert Class Field Towers with Prescribed Galois Groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911101532241920 |
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| author | Maire, Christian Sankara, Karim |
| author_facet | Maire, Christian Sankara, Karim |
| contents | In this work, we show that given a finite p-group G, a number field K having a trivial p-class group Cl K , and a finite set of primes S of K, there exists a finite extension F/K such that the S-split p-Hilbert class field tower L S p (F ) of F has G as its Galois group. This extends results by Ozaki and Hajir-Maire-Ramakrishna. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On S-Split p-Hilbert Class Field Towers with Prescribed Galois Groups Maire, Christian Sankara, Karim Number Theory In this work, we show that given a finite p-group G, a number field K having a trivial p-class group Cl K , and a finite set of primes S of K, there exists a finite extension F/K such that the S-split p-Hilbert class field tower L S p (F ) of F has G as its Galois group. This extends results by Ozaki and Hajir-Maire-Ramakrishna. |
| title | On S-Split p-Hilbert Class Field Towers with Prescribed Galois Groups |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.07946 |