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+ 𝜀n−1)) 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+ 𝜀n−1))?” 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.
