Group theory of cyclic cubic number fields
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914830586216448 |
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| author | Mayer, Daniel C. Aouissi, Siham Allombert, Bill Soullami, Abderazak |
| author_facet | Mayer, Daniel C. Aouissi, Siham Allombert, Bill Soullami, Abderazak |
| contents | Astonishing new discoveries with quartets and octets of cyclic cubic fields sharing a common conductor are presented. Four kinds of graphs describing cubic residue conditions among the prime divisors of the conductor enforce elementary bi- or tricyclic 3-class groups and either a metabelian 3-class field tower group of coclass at least two or a closed Andozhskii-Tsvetkov group of order 6561. In the latter situation, abelian type invariants of first and second order are required for the identification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06030 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Group theory of cyclic cubic number fields Mayer, Daniel C. Aouissi, Siham Allombert, Bill Soullami, Abderazak Number Theory 11R16, 11R27, 11R29, 11R32, 11R37, 20D15, 20F05 Astonishing new discoveries with quartets and octets of cyclic cubic fields sharing a common conductor are presented. Four kinds of graphs describing cubic residue conditions among the prime divisors of the conductor enforce elementary bi- or tricyclic 3-class groups and either a metabelian 3-class field tower group of coclass at least two or a closed Andozhskii-Tsvetkov group of order 6561. In the latter situation, abelian type invariants of first and second order are required for the identification. |
| title | Group theory of cyclic cubic number fields |
| topic | Number Theory 11R16, 11R27, 11R29, 11R32, 11R37, 20D15, 20F05 |
| url | https://arxiv.org/abs/2406.06030 |