Geodesic
Real quadratic number fields with metacyclic Hilbert $2$-class field tower
Mathematica Bohemica, Tome 144 (2019) no. 2, pp. 177-190.

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We begin by giving a criterion for a number field $K$ with 2-class group of rank 2 to have a metacyclic Hilbert 2-class field tower, and then we will determine all real quadratic number fields $\mathbb Q(\sqrt d)$ that have a metacyclic nonabelian Hilbert $2$-class field tower.
DOI : 10.21136/MB.2018.0102-17
Classification : 11R11, 11R29, 11R37
Keywords: class field tower; class group; real quadratic number field; metacyclic group 
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Essahel, Said; Dakkak, Ahmed; Mouhib, Ali. Real quadratic number fields with metacyclic Hilbert $2$-class field tower. Mathematica Bohemica, Tome 144 (2019) no. 2, pp. 177-190. doi : 10.21136/MB.2018.0102-17. http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0102-17/

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