Minimal discriminants for fields with small Frobenius groups as Galois groups

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Abstract

We apply class field theory to the computation of the minimal discriminants for certain solvable groups. In particular, we apply our techniques to small Frobenius groups and all imprimitive degree 8 groups such that the corresponding fields have only a degree 2 and no degree 4 subfield.

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Part of this article was written during a visit by the author to the Computational Algebra Group at the University of Sydney in September, 2001.