International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 1-4
doi:10.1155/S0161171288000018

Quadratic subfields of quartic extensions of local fields

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