Let M/F and K/F be Galois extensions with Galois groups G =Gal(M/F) and H = Gal(K/F). Since M/F is Galois, and K/F is a fieldextension, we have the composite extension field K M.
Show that σ → (σ|M , σ|K) is ahomomorphism from Gal(K M/F) to G × H, and that it is one-to-one.[As in the notes, σ|X means the restriction of the map σto the subset X of its domain.]
