The Absolute Galois Group of a Semi-Local Field

<p>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.</p><p>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. </p><p> The book will be of interest to researchers in field arithmetic Galois theory and profinite groups.</p><br><br>