ABSTRACT
The purpose of this chapter is to study finite extensions which are simultaneously Galois and G-Cogalois. In Section 5.1 we characterize G- radical extensions, not necessarily finite, which are separable or Galois. In the next section we prove that the Kneser group and the Galois group of any finite Abelian G-Cogalois extension are isomorphic, but not in a canonical way. Section 5.3 contains some applications of Section 5.1 and Section 5.2 to elementary Field Arithmetic. Further applications, involving results we will prove in Section 6.1, Chapter 7, and Section 8.1 will be given in Section 8.2.
