On the maximal unramified pro-2-extension over the cyclotomic -extension of an imaginary quadratic field
Yasushi Mizusawa (2010)
Journal de Théorie des Nombres de Bordeaux
Similarity:
For the cyclotomic -extension of an imaginary quadratic field , we consider the Galois group of the maximal unramified pro--extension over . In this paper, we give some families of for which is a metabelian pro--group with the explicit presentation, and determine the case that becomes a nonabelian metacyclic pro--group. We also calculate Iwasawa theoretically the Galois groups of -class field towers of certain cyclotomic -extensions.