Titlebook: Galois Theory Through Exercises; Juliusz Brzeziński Textbook 2018 Springer International Publishing AG, part of Springer Nature 2018 Galoi

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Cemal Cingi,Arzu Yorganc?o?lu,Alvaro A. Cruzalois groups of its reductions modulo prime numbers. Several exercises are concerned with Dedekind’s theorem, allowing for the construction of polynomials with given Galois groups and the solution of the inverse problem for the symmetric group S..

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bibliophile

Separable Extensions,ove the theorem on primitive element which says that a finite separable extension can be generated over its ground field by only one element. This theorem is usually part of any standard course on the subject.

bibliophile

起皺紋

Computing Galois Groups,alois groups of its reductions modulo prime numbers. Several exercises are concerned with Dedekind’s theorem, allowing for the construction of polynomials with given Galois groups and the solution of the inverse problem for the symmetric group S..

Bouquet

Cyclotomic Extensions,their properties, which find different applications in number theory and algebra. Among many applications, there is a proof of a special case of Dirichlet’s theorem on primes in arithmetic progression using the cyclotomic polynomials. This chapter also includes an exercise on a solution of the inverse Galois problem for all abelian groups.

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