Some results related to Hilbert's theorem 94
Abstract
Let K be a cyclic unramified extension of a number field F. Hilbert's theorem 94 implies that a nonprincipal ideal class of F becomes principal in K. Say, K/F satisfies condition (B) if no element of the subgroup of the ideal class group of F corresponding to the extension K/F becomes principal in K. Then K/F satisfies condition (B) if, and only if, the cohomology of the ideal class group of K is trivial. If F is a quadratic field for which the Sylow p subgroup of the ideal class group is of type (p, p), then some results on the structure of the ideal class group of K are obtained.
- Publication:
-
Journal of Number Theory
- Pub Date:
- May 1970
- DOI:
- 10.1016/0022-314X(70)90020-X
- Bibcode:
- 1970JNT.....2..199K