Induced ^-elements in the Schur Group
نویسنده
چکیده
The main result of this paper gives necessary and sufficient conditions for the ^-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 nth root of unity. Moreover we completely answer the question: "When is SiQiεn + ε-)) 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 -f ε; ))?" 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.
منابع مشابه
Characterization of finite $p$-groups by the order of their Schur multipliers ($t(G)=7$)
Let $G$ be a finite $p$-group of order $p^n$ and $|{mathcal M}(G)|=p^{frac{1}{2}n(n-1)-t(G)}$, where ${mathcal M}(G)$ is the Schur multiplier of $G$ and $t(G)$ is a nonnegative integer. The classification of such groups $G$ is already known for $t(G)leq 6$. This paper extends the classification to $t(G)=7$.
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