TY - BOOK ID - 2760500 TI - Profinite groups AU - Ribes, Luis AU - Zalesskii, Pavel PY - 2000 VL - 3. Folge, v. 40 SN - 3540669868 3642086322 3662040972 PB - New York ; Berlin ; Heidelberg Springer DB - UniCat KW - Groupes profinis KW - Profinite groups KW - Profinite groups. KW - 512.54 KW - Groups. Group theory KW - 512.54 Groups. Group theory KW - Group theory KW - Group theory. KW - Topological groups. KW - Lie groups. KW - Number theory. KW - Topology. KW - Group Theory and Generalizations. KW - Topological Groups, Lie Groups. KW - Number Theory. KW - Analysis situs KW - Position analysis KW - Rubber-sheet geometry KW - Geometry KW - Polyhedra KW - Set theory KW - Algebras, Linear KW - Number study KW - Numbers, Theory of KW - Algebra KW - Groups, Lie KW - Lie algebras KW - Symmetric spaces KW - Topological groups KW - Groups, Topological KW - Continuous groups KW - Groups, Theory of KW - Substitutions (Mathematics) UR - https://www.unicat.be/uniCat?func=search&query=sysid:2760500 AB - The aim of this book is to serve both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. In neither of these two aspects have we tried to be encyclopedic. After some necessary background, we thoroughly develop the basic properties of profinite groups and introduce the main tools of the subject in algebra, topology and homol­ ogy. Later we concentrate on some topics that we present in detail, including recent developments in those areas. Interest in profinite groups arose first in the study of the Galois groups of infinite Galois extensions of fields. Indeed, profinite groups are precisely Galois groups and many of the applications of profinite groups are related to number theory. Galois groups carry with them a natural topology, the Krull topology. Under this topology they are Hausdorff compact and totally dis­ connected topological groups; these properties characterize profinite groups. Another important fact about profinite groups is that they are determined by their finite images under continuous homomorphisms: a profinite group is the inverse limit of its finite images. This explains the connection with abstract groups. If G is an infinite abstract group, one is interested in deducing prop­ erties of G from corresponding properties of its finite homomorphic images. ER -