Quadratic subfields on quartic extensions of local fields

Joe Repka

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-4

Abstract:

We show that any quartic extension of a local field of odd residue characteristic must contain an intermediate field. A consequence of this is that local fields of odd residue characteristic do not have extensions with Galois group A 4 or S 4 . Counterexamples are given for even residue characteristic.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:575432

DOI: 10.1155/S0161171288000018

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