Fri Apr 20

Finite fields are Galois over F_p. The Galois group is generated by the Frobenius.

Nailed down the Galois correspondence. Lemma: If F > E > H > K, E > H is finite, and H''=H, then E''=E. Galois correspondence when applied to H=K.

An extension is Galois iff the Galois group is big enough.

Normal subgroups <-> subfields E stable under the Galois group, which in turn implies that F/E, E/K are Galois extensions, and there is a short exact sequence of Galois groups.