Generators for the schur group of local and global number fields

Abstract

The main result of this paper gives a set of generators for the Schur group, S(K), for any subfield X of a cyclotomic extension of the rational field. This result is obtained from two reduction theorems which apply to more general fields. In particular we use them to derive in a rather simple way the results of T. Yamada which determine S(k) when k is a p-adic number field. Some new results are given in the case K is a subfield of Q(ϵm) and Q(ϵm) is unramified over K. An example is given to show how the Riemann hypothesis may enter into the computation of S(K) when Q(ϵm) is ramified over K. © 1975 Pacific Journal of Mathematics.