A Group Theoretic Approach to Cyclic Cubic Fields-Reference-Cited by-同舟云学术

A Group Theoretic Approach to Cyclic Cubic Fields

Published:2023-12-29 Issue:1 Volume:12 Page:126
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Aouissi Siham¹,Mayer Daniel C.²^ORCID

Affiliation:

1. Algebraic Theories and Applications Research Team (ATA), Ecole Normale Supèrieure of Moulay Ismail University (ENS-UMI), ENS, Toulal, Meknès B.P. 3104, Morocco

2. Independent Researcher, Naglergasse 53, 8010 Graz, Austria

Abstract

Let (kμ)μ=14 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 of the quartet whose 3-class group Cl3(kμ)≃(Z/3Z)2 is elementary bicyclic, the automorphism group M=Gal(F32(kμ)/kμ) of the maximal metabelian unramified 3-extension of kμ 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 kμ. With the aid of the relation rank d2(M), it is decided whether M coincides with the Galois group G=Gal(F3∞(kμ)/kμ) of the maximal unramified pro-3-extension of kμ.

Funder

Austrian Science Fund

Research Executive Agency of the European Union

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/12/1/126/pdf

Reference26 articles.

1. Sur les ℓ-classes d’idéaux dans les extensions cycliques relatives de degré premier ℓ;Gras;Ann. Inst. Fourier,1973

2. Ayadi, M. (1995). Sur la capitulation des 3-classes d’idéaux d’un corps cubique cyclique. [Ph.D. Thesis, Université Laval].

3. Besche, H.U., Eick, B., and O’Brien, E.A. (2005). The SmallGroups Library—A Library of Groups of Small Order, Magma.

4. Bicyclic Bicubic Fields;Parry;Canad. J. Math.,1990

5. Multiplicities of dihedral discriminants;Mayer;Math. Comp.,1992

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1. A Group Theoretic Approach to Cyclic Cubic Fields;Mathematics;2023-12-29