Vol. 90, No. 1, 1980

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Induced p-elements in the Schur group

Richard A. Mollin

Vol. 90 (1980), No. 1, 169–176

The main result of this paper gives necessary and sufficient conditions for the p-primary part S(K)p of the Schur group S(K) to be induced from S(F)p for any subfield F of K where K is contained in Q(𝜀n), under the restriction that 𝜀p2 is not in K if p > 2 and n is odd if p = 2, where 𝜀n is a primitive n-th root of unity.

Moreover we completely answer the question: “When is S(Q(𝜀n + 𝜀n1)) induced from S(Q)?” for any n, and also the question: “When are the quaternion division algebras in S(Q(𝜀n)) induced from S(Q(𝜀n + 𝜀n1))?” for any n. Finally, in the last section we investigate the “generalized group of algebras with uniformly distributed invariants” which we introduced in an earlier paper. We obtain, for the first time, a sufficient condition for the group to be induced from a certain subgroup.

Mathematical Subject Classification 2000
Primary: 16A26, 16A26
Secondary: 13A20, 20C99, 12A80
Received: 10 November 1977
Revised: 28 August 1979
Published: 1 September 1980
Richard A. Mollin
Department of Mathematics and Statistics
University of Calgary
Calgary T2N 1N4