ABSTRACT
The aim of this chapter is to investigate the Cogalois extensions, introduced into the literature in 1986 by Greither and Harrison [ 63 ]. Using the concept of Kneser extension, a finite extension E/F is a Cogalois extension precisely when it is https://www.w3.org/1998/Math/MathML"> T ( E / F ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175695/6f0d74fd-b81c-4cd4-b8d9-805c7c0522ee/content/eq1551.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> -Kneser. We defined in Section 2.1 the Cogalois group of an extension E/F as being the group https://www.w3.org/1998/Math/MathML"> T ( E / F ) / F * https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175695/6f0d74fd-b81c-4cd4-b8d9-805c7c0522ee/content/eq1552.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and we denoted it by https://www.w3.org/1998/Math/MathML"> C o g ( E / F ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175695/6f0d74fd-b81c-4cd4-b8d9-805c7c0522ee/content/eq1553.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . Thus, a finite radical extension E/F is Cogalois if and only if https://www.w3.org/1998/Math/MathML"> | C o g ( E / F ) | = [ E : F ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175695/6f0d74fd-b81c-4cd4-b8d9-805c7c0522ee/content/eq1554.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> .
