Group theory of cyclic cubic number fields

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Mayer, Daniel C, Aouissi, Siham, Allombert, Bill, Soullami, Abderazak
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.06.2024
Subjects
Conductors
Fields (mathematics)
Group theory
Number theory
Octets
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Summary: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.
ISSN:2331-8422