A finite normal extension K of a field F is cyclic over F if G(K/F) is a cyclic group.
a. Show that if K is cyclic over F and E is a normal extension of F, where F ≤ E ≤ K, then E is cyclic over F and K is cyclic over E.
b. Show that if K is cyclic over F, then there exists exactly one field E, F ≤ E ≤ K, of degree d over F for each divisor d of [K : F].