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Contemporary Galois theory and its classical problems
Mathematics and Education in Mathematics, Tome 52 (2023), pp. 76-87 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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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. В това проучване очертаваме крайъгълните камъни на няколко класически проблема в теорията на Галоа: ньотеровата задача, обратната задача и задачата за вложимост. Демонстрираме връзката между тези проблеми в по-широкия контекст на теория на инвариантите на крайните групи. Също така посочваме няколко нови резултата на автора и неговите сътрудници по отношение на ньотеровата задача и задачата за вложимост.
Keywords: Noether’s problem, the embedding problem, Galois group, the inverse problem, 12F12, 13A50, 20D15, 14E08, Ньотеровата задача, задачата за вложимост, група на Галоа, обратната задача, 12F12, 13A50, 20D15, 14E08 
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Michailov, Ivo. Contemporary Galois theory and its classical problems. Mathematics and Education in Mathematics, Tome 52 (2023), pp. 76-87. http://geodesic.mathdoc.fr/item/MEM_2023_52_a5/