Problems in Galois Theory a Let K be a field of characteristic p > 0, and let c in K Show that if

Problems in Galois Theory

a Let K be a field of characteristic p > 0, and let c in
K Show that if alpha is a root of f (x) = x^p – x – c, so is alpha + 1 Prove
that K(alpha) is Galois over K with group either trivial or cyclic of order p

b Find all subfields of Q ( sqrt2, sqrt 3) with proof that
you have them all What is the minimal polynomial of sqrt2+ sqrt3? Which
subfields does it generate over Q?