ABSTRACT
This chapter contains the main results of Part I of the monograph. The notions of Cogalois connection, strongly G-Kneser extension, and G Cogalois extension are introduced. The last ones are those separable G- Kneser extensions E/F for which there exists a canonical lattice isomorphism between the lattice of all subextensions of E/F and the lattice of all subgroups of the group https://www.w3.org/1998/Math/MathML"> G / F * https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175695/6f0d74fd-b81c-4cd4-b8d9-805c7c0522ee/content/eq2048.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . A very useful characterization of G-Cogalois extensions in terms of n-purity is given, where n is the exponent of the finite group https://www.w3.org/1998/Math/MathML"> G / F * https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175695/6f0d74fd-b81c-4cd4-b8d9-805c7c0522ee/content/eq2049.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . Using this characterization, we will show in Chapter 7 that the class of G-Cogalois extensions is large enough, including important classes of finite extensions.
