Group theoretic approach to cyclic cubic fields

Autor: Aouissi, Siham, Mayer, Daniel C.
Rok vydání: 2023
Předmět:
Zdroj: Mathematics, Volume 12, Issue 1, 126 (2024)
Druh dokumentu: Working Paper
DOI: 10.3390/math12010126
Popis: Let (k1,k2,k3,k4) be a quartet of cyclic cubic number fields sharing a common conductor c=pqr divisible by exactly three prime(power)s p,q,r. For those components k of the quartet whose 3-class group Cl(3,k) = Z/3Z x Z/3Z is elementary bicyclic, the automorphism group M = Gal(F(3,2,k)/k) of the maximal metabelian unramified 3-extension of k is determined by conditions for cubic residue symbols between p,q,r and for ambiguous principal ideals in subfields of the common absolute 3-genus field k* of k1,k2,k3,k4. With the aid of the relation rank d2(M), it is decided whether M coincides with the Galois group G = Gal(F(3,infinity,k)/k) of the maximal unramified pro-3-extension of k.
Comment: 46 pages, 21 tables
Databáze: arXiv
Externí odkaz:
Nepřihlášeným uživatelům se plný text nezobrazuje