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International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 1-4

Quadratic subfields on quartic extensions of local fields

Mathematics Department, University of Toronto, Ontario, Toronto M5S 1A1, Canada

Received 18 March 1987

Copyright © 1988 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 A4 or S4. Counterexamples are given for even residue characteristic.