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. The book is reasonably self-contained. Profinite groups are Galois groups. As such they are of interest in algebraic number theory. Much of recent research on abstract infinite groups is related to profinite groups because residually finite groups are naturally embedded in a profinite group. In addition to basic facts about general profinite groups, the book emphasizes free constructions (particularly free profinite groups and the structure of their subgroups). Homology and cohomology is described with a minimum of prerequisites.
Table of contents:
Inverse and Direct Limits.- Profinite Groups.- Free Profinite Groups.- Some Special Profinite Groups.- Discrete and Profinite Modules.- Homology and Cohomology of Profinite Groups.- Cohomological Dimension.- Normal Subgroups of Free Pro-C Groups.- Free Constructions.- Open Questions.- Appendix.- Bibliography.
Table of contents:
Inverse and Direct Limits.- Profinite Groups.- Free Profinite Groups.- Some Special Profinite Groups.- Discrete and Profinite Modules.- Homology and Cohomology of Profinite Groups.- Cohomological Dimension.- Normal Subgroups of Free Pro-C Groups.- Free Constructions.- Open Questions.- Appendix.- Bibliography.
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)
"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)
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)