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 Joe Repka. 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 or . Counterexamples are given for even residue characteristic.