Luis Ribes, Pavel Zalesskii

eBook, PDF

Profinite Groups (eBook, PDF)

Beschreibung

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.

Technische Details

• Geräte: PC
• ohne Kopierschutz
• Größe: 34.84MB

Barrierefreiheit

• Text-to-Speech

Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 435
• Erscheinungstermin: 9. April 2013
• Englisch
• ISBN-13: 9783662040973
• Artikelnr.: 53136597

Rezensionen

From the reviews of the second edition:

"In this book, Ribes and Zalesskii survey the general theory of profinite groups ... . They cover all the important examples and do a particularly fine job of explaining the representation theory and the cohomology theory of profinite groups. ... Each chapter concludes with an extensive section of notes, including recent developments and open questions. ... It will be extremely useful to researchers in field and even more so to those who (like me) use profinite groups in their own work."

(Fernando Q. Gouvêa, The Mathematical Association of America, August, 2010)

"The book has an extensive bibliography, which appears to be remarkably complete, up to the very recent developments. An excellent guide to this vast amount of literature is provided by the closing sections of each chapter ... . the many important and current topics dealt with here are treated with admirable completeness and clarity ... . The book is very valuable as a reference work, and offers several excellent choices as a textbook for a graduate course." (A.Caranti, zbMATH 0949.20017, 2022)

From the reviews of the second edition:

"In this book, Ribes and Zalesskii survey the general theory of profinite groups ... . They cover all the important examples and do a particularly fine job of explaining the representation

theory and the cohomology theory of profinite groups. ... Each chapter concludes with an extensive section of notes, including recent developments and open questions. ... It will be extremely useful to researchers in field and even more so to those who (like me) use profinite groups in their own work." (Fernando Q. Gouvêa, The Mathematical Association of America, August, 2010)

"This valuable book works well both as an introduction to the subject of profinite groups, and as a reference for some specific areas. This second edition presents an updated and enlarged bibliography. More open questions have been added, and solutions are provided for the problems from the previous edition that have been settled since." (A. Caranti, Zentralblatt MATH, Vol. 1197, 2010)