Vol. 69, No. 1, 1977

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Calculations of the Schur group

James William Pendergrass

Vol. 69 (1977), No. 1, 169–175

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
Received: 14 February 1975
Published: 1 March 1977
James William Pendergrass