Maximal unramified extensions of imaginary quadratic number fields of small conductors, by Ken Yamamura

In this paper we determine the structure of the Galois groups of the maximal unramified extensions of imaginary quadratic number fields of conductors less than 1000 under GRH except some fields. For only 12 fields among 305 such fields, the maximal unramified extension contains the Hilbert class field of the genus field as a proper subfield. For 275 fields among the other 293 fields, we have checked the maximal unramified extension coincides with the Hilbert class field of the genus field. (Probably, so are the other 18 fields, however, this has not been proved yet.)

Ken Yamamura <yamamura@cc.nda.ac.jp>