The Schur subgroup of the Brauer group

James William Pendergrass

Vol. 69 (1977), No. 2, 477–499

DOI: 10.2140/pjm.1977.69.477

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.

Mathematical Subject Classification

Primary: 13A20

Milestones

Received: 18 November 1974

Published: 1 April 1977