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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

The construction of unramified cyclic quartic extensions of $ Q(\sqrt m)$


Author: Theresa P. Vaughan
Journal: Math. Comp. 45 (1985), 233-242
MSC: Primary 11R11; Secondary 11R29
DOI: https://doi.org/10.1090/S0025-5718-1985-0790656-6
MathSciNet review: 790656
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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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DOI: https://doi.org/10.1090/S0025-5718-1985-0790656-6
Article copyright: © Copyright 1985 American Mathematical Society