Paper 2, Section II, H
Part II, 2016
(a) Let be a finite separable field extension. Show that there exist only finitely many intermediate fields .
(b) Define what is meant by a normal extension. Is a normal extension? Justify your answer.
(c) Prove Artin's lemma, which states: if is a field extension, is a finite subgroup of , and is the fixed field of , then is a Galois extension with .