Suppose K is a Galois extension of F of degree for some prime p and some . Show there are Galois extensions of F contained in K of degrees and .
So what I want is Fields or
From the fundemental theorem of Galois I get the two diagrams relating the groups to the fields
according to another part of the fundemental theorem I get
I get that is Galios over F iff is a normal subgroup of of G.
For some reason I think that G must be cyclic but I can't prove why. If that Is the case I am done.