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Let M/F and K/F be Galois extensions with Galois groups G = Gal(M/F) and H =...

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 field extension, we have the composite extension field K M

Show that the image is {(τ, υ) ∈ G × H | τ |K∩M = υ|K∩M }

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