Azizi, A. and Zekhnini, A. and Taous, M. (2016) Coclass of Gal(k(2)2/k) for some fields k = Q(√p1p2q, √1) with 2-class groups of types (2, 2, 2). Journal of Algebra and its Applications, 15 (2).

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Abstract

Let p1 =p2 = .q =1 (mod 4) be primes such that (2 p1 ) = 1 and (2/p2 ) = (p1/p2 ) = (p1/q ) = Put i = √ .1 and d = p1p2q, then the bicyclic biquadratic field k = Q(ã d, i) has an elementary Abelian 2-class group of rank 3. In this paper we determine the nilpotency class, the coclass, the generators and the structure of the non-Abelian Galois group Gal(k(2)2/k) of the second Hilbert 2-class field k(2) 2 of k, we study the 2-class field tower of k, and we study the capitulation problem of the 2-classes of k in its fourteen abelian unramified extensions of relative degrees two and four. © 2016 World Scientific Publishing Company.

Item Type: Article
Subjects: Mathematics
Divisions: SCIENTIFIC PRODUCTION > Mathematics
Depositing User: Administrateur Eprints Administrateur Eprints
Last Modified: 31 Jan 2020 15:48
URI: http://eprints.umi.ac.ma/id/eprint/4013

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