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arXiv · 2406.06030

Group theory of cyclic cubic number fields

Daniel C. Mayer·Siham Aouissi·Bill Allombert·Abderazak Soullami
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Abstract

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.

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Daniel C. Mayer, Siham Aouissi, Bill Allombert, Abderazak Soullami. 2024-06-10. Group theory of cyclic cubic number fields. https://arxiv.org/abs/2406.06030

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