CH 5- Galois Groups and the Fundamental Theorem of Galois Theory

Question 1

Define an automorphism of a field.

Define an F-homomorphism/ F-automorphism.

Define the Galois Group.

Answer 1

Question 2

State and prove a lemma on applying field homomorphisms to roots.

State and prove a corollary about the Galois group Gal(K/F) and the symmetric group S_n.

Answer 2

Question 3

State two lemmas on counting homomorphisms between different fields.

State and prove a theorem on the size of the Galois group for normal/separable/finite extensions.

Answer 3

Question 4

Define a Galois extension.

State a lemma on intermediate fields and Galois extensions.

Answer 4

Question 5

5.2. The Galois correspondence page 56 onwards. - CHECK OLD LEMMAS FOR THE UPDATE