The construction of unramified cyclic quartic extensions of 𝑄(√𝑚)

Vaughan, Theresa P.

doi:10.1090/S0025-5718-1985-0790656-6

The construction of unramified cyclic quartic extensions of $Q(\sqrt m)$
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Math. Comp. 45 (1985), 233-242 Request permission

Abstract:

We give an elementary general method for constructing fields K satisfying $[K:Q] = 8$, the Galois group of K over Q is dihedral, and K is unramified over one of its quadratic subfields. Given an integer m, we describe all such fields K which contain $Q(\sqrt m )$. The description is specific and is given in terms of the arithmetic of the quadratic subfields of K.

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