Calculations of the Schur group

James William Pendergrass

Vol. 69 (1977), No. 1, 169–175

DOI: 10.2140/pjm.1977.69.169

Abstract

Let the field K be an abelian extension of the rational field Q. The Schur group of K, S(K), consists of those classes in the Brauer group of K which contain an algebra isomorphic to a simple component of a rational group algebra QG for some finite group G.

Suppose that K has a cyclic extension of the form Q(ζ) where ζ is a primitive n-th root of unity. In this paper we calculate the 2-part of S(K) where K contains the fourth roots of unity.

Mathematical Subject Classification 2000

Primary: 12A60, 12A60

Secondary: 20C05

Milestones

Received: 14 February 1975

Published: 1 March 1977