Abstract
Let be an imaginary quadratic field with . It is known that the length of the Hilbert -class field tower is at least . Gerth (On 2-class field towers for quadratic number fields with -class group of type , Glasgow Math. J. 40(1) (1998), 63-69) calculated the density of where the length of the tower is ; that is, the maximal unramified -extension is a -extension. In this paper, we shall extend this result for generalized quaternion, dihedral, and semidihedral extensions of small degrees.
Original language | English |
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Pages (from-to) | 166-187 |
Number of pages | 22 |
Journal | Nagoya Mathematical Journal |
Volume | 237 |
DOIs | |
Publication status | Published - 2020 Mar 1 |
ASJC Scopus subject areas
- Mathematics(all)