Section outline

  • We defined maps \mathcal{G} and \mathcal{F} between subfields of a field K and subgroups of \mathrm{Aut}(K). We proved properties of the maps. In particular, we proved that the maps define inclusion an reversing correspondence between subfields of K of the form \mathcal{F}(H) for some subgroup H \leq \mathrm{Aut}(K) and the subgroups of \mathrm{Aut}(K) of the form \mathcal{G}(L) for some subfield of K.  

    We proved the Fundamental Theorem of Galois Theory and saw examples.

    Reading: section 2.4, pages 23-26 from the notes.