Mark each of the following true or false.
___ a. Two different subgroups of a Galois group may have the same fixed field.
___ b. In the notation of Theorem 53.6, if F ≤ E < L ≤ K, then λ(E) < λ(L).
___ c. If K is a finite normal extension of F, then K is a normal extension of E, where F ≤ E ≤ K.
___ d. If two finite normal extensions E and L of a field F have isomorphic Galois groups, then [E : F] = [L: F].
___ e. If E is a finite normal extension of F and H is a normal subgroup of G(E/F), then E_H is a normal extension of F.
___ f. If E is any finite normal simple extension of a field F, then the Galois group G(E/F) is a simple group.
___ g. No Galois group is simple.
___ h. The Galois group of a finite extension of a finite field is abelian.
___ i. An extension E of degree 2 over a field F is always a normal extension of F.
___ j. An extension E of degree 2 over a field F is always a normal extension of F if the characteristic of F is not 2.