Profinite Groups - Blackwell's Bookshop Online

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. This second edition contains three new appendices dealing with a new characterization of free profinite groups, presentations of pro-p groups and a new conceptually simpler approach to the proof of some classical subgroup theorems. Throughout the text there are additions in the form of new results, improved proofs, typographical corrections, and an enlarged bibliography. The list of open questions has been updated; comments and references have been added about those previously open problems that have been solved after the first edition appeared.

ISBN	3642016413	Weight (grammes)	877
ISBN13	9783642016417 (What's this?)	Published in	Berlin
Publisher	Springer-Verlag Berlin and Heidelberg GmbH & Co. KG	Series title	Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of
Imprint	Springer-Verlag Berlin and Heidelberg GmbH & Co. K	Previous ISBN	9783540669869
Format	Hardback	Height (mm)	234
Publication date	28 Feb 2010	Width (mm)	156
DEWEY	512.2	Spine width (mm)	26
DEWEY edition	DC22	Academic level	Professional / Scholarly
Pages	482

1		Inverse and Direct Links
2		Profinite Groups
3		Free Profinite Groups
4		Some Special Profinite Groups
5		Discrete and Profinite Modules
6		Homology and Cohomology of Profinite Groups
7		Cohomological Dimension
8		Normal Subgroups of Free Pro-C Groups
9		Free Constructions of Profinite Groups
		Open Questions
App. A		Spectral Sequences
App. B		A Different Characterization of Free Profinite Groups
App. C		Presentations of Profinite Groups
App. D		Wreath Products and Some Subgroup Theorems
		Bibliography
		Index of Symbols
		Index of Authors
		Index of Terms

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. Gouvea, 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)

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