\(2\)-Galois groups and the Kaplansky radical

• Date: 2018
• Main Authors: Dario, Ronie Peterson, Engler, Antonio Jose
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Brauer group; free pro-\(2\) product; Galois group; \(2\)-henselian valuation ring; quadratic form; 12J10; 12F10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/649
• Journal Title: Algebra and Discrete Mathematics

An accurate description of the Galois group \(G_{F}(2)\) of the maximal Galois \(2\)-extension of a field \(F\) may be given for fields \(F\) admitting a \(2\)-henselian valuation ring. In this note we generalize this result by characterizing the fields for which \({G_{F}{(2)}}\) decomposes as a fre...