Mathematica Bohemica, Vol. 144, No. 2, pp. 177-190, 2019
Real quadratic number fields with metacyclic Hilbert 2-class field tower
Said Essahel, Ahmed Dakkak, Ali Mouhib
Received September 7, 2017. Published online August 30, 2018.
Abstract: 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 $\Q(\sqrt d) $ that have a metacyclic nonabelian Hilbert 2-class field tower.
Keywords: class field tower; class group; real quadratic number field; metacyclic group
Affiliations: Said Essahel, Ahmed Dakkak, Ali Mouhib, Sidi Mohammed Ben Abdellah University, Sciences and Engineering Laboratory, Polydisciplinary Faculty of Taza, Taza-Gare PB 1223, Taza, Morocco, e-mail: essahel69@yahoo.fr, dakkakahmed@hotmail.com, mouhibali@yahoo.fr