文摘
Let k be a real quadratic number field with 2-class group C2(k)C2(k) isomorphic to Z/2mZxZ/2nZ, m≥1m≥1, n≥2n≥2, and let k1k1 be the Hilbert 2-class field of k. We give complete criteria for C2(k1)C2(k1) to be cyclic when either dkdk, the discriminant of k, is divisible by only positive prime discriminants, or when the 2-class number of k1k1 is greater than 2, and partial criteria for C2(k1)C2(k1) to be elementary cyclic when dkdk is divisible by a negative prime discriminant.