The schur subgroup of the brauer group

Abstract

Let K be a subfield of a cyclotomic extension L of the rational field Q. The Schur subgroup, S(K), of the Brauer group of K, B(K), consists of those algebra classes which contain an algebra which is isomorphic to a simple component of a group algebra QG for some finite group G. In this paper we describe a set of generators for S(K). We then use this theorem to determine the 2-primary part of S(K) when L/K is cyclic and the fourth roots of unity are not in K. © 1977 Pacific Journal of Mathematics. All rights reserved.