Съвременна теория на Галоа и нейните класически задачи

Abstract

[Michailov Ivo M.; Михайлов Иво М.]In this survey we outline the milestones of several classical problems in Galois theory: Noether’s problem, the inverse problem and the embedding problem. We demonstrate the connection between these problems in the bigger context of the invariant theory of finite groups. We also point out several new results of the author and his collaborators regarding Noether’s problem and the embedding problem. 2020 Mathematics Subject Classification: 12F12, 13A50, 20D15, 14E08