We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
A Group Theoretic Approach to Cyclic Cubic Fields.
- Authors
Aouissi, Siham; Mayer, Daniel C.
- Abstract
Let (k μ) μ = 1 4 be a quartet of cyclic cubic number fields sharing a common conductor c = p q r divisible by exactly three prime(power)s, p , q , r . For those components of the quartet whose 3-class group Cl 3 (k μ) ≃ (Z / 3 Z) 2 is elementary bicyclic, the automorphism group M = Gal (F 3 2 (k μ) / k μ) of the maximal metabelian unramified 3-extension of k μ 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 all k μ . With the aid of the relation rank d 2 (M) , it is decided whether M coincides with the Galois group G = Gal (F 3 ∞ (k μ) / k μ) of the maximal unramified pro-3-extension of k μ .
- Subjects
AUTOMORPHISM groups; CLASS groups (Mathematics); MAXIMAL subgroups; GALOIS theory; MORPHISMS (Mathematics)
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 1, p126
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12010126