Produktdetaljer
ISBN
9783030891909
Publisert
2021-11-20
Utgiver
Springer Nature Switzerland AG
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
16
Its main result, a theorem proved by the authors and Florian Pop in 2012, describes the absolute Galois group of distinguished semi-local algebraic (and other) extensions of the rational numbers as free products of the free profinite group on countably many generators and local Galois groups.
Les mer
This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers. Its main result, a theorem proved by the authors and Florian Pop in 2012, describes the absolute Galois group of distinguished semi-local algebraic (and other) extensions of the rational numbers as free products of the free profinite group on countably many generators and local Galois groups. This is an instance of a positive answer to the generalized inverse problem of Galois theory.
Adopting both an arithmetic and probabilistic approach, the book carefully sets out the preliminary material needed to prove the main theorem and its supporting results. In addition, it includes a description of Melnikov's construction of free products of profinite groups and, for the first time in book form, an account of a generalization of the theory of free products of profinite groups and their subgroups.
The book will be of interest to researchers in fieldarithmetic, Galois theory and profinite groups.
Les mer
Presents the structure of the absolute Galois groups of distinguished algebraic extensions of the rational numbers Treats Galois theory and profinite groups from both an arithmetic and probabilistic point of view Contains results on free products of profinite groups which appear here for the first time in book form
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Les mer
Produktdetaljer
ISBN
9783030891909
Publisert
2021-11-20
Utgiver
Springer Nature Switzerland AG
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
16