Profinite Groups

The aim of this book is to serve both as an introduction to profinite groupsand as a reference for specialists in some areas of the theory. The book isreasonabl... » 

The aim of this book is to serve both as an introduction to profinite groupsand as a reference for specialists in some areas of the theory. The book isreasonably selfcontained. Profinite groups are Galois groups. As such they areof interest in algebraic number theory. Much of recent research on abstractinfinite groups is related to profinite groups because residually finite groupsare naturally embedded in a profinite group. In addition to basic facts aboutgeneral profinite groups the book emphasizes free constructions particularlyfree profinite groups and the structure of their subgroups. Homology andcohomology is described with a minimum of prerequisites. This second editioncontains three new appendices dealing with a new characterization of freeprofinite groups presentations of prop groups and a new conceptually simplerapproach to the proof of some classical subgroup theorems. Throughout the textthere are additions in the form of new results improved proofs typographicalcorrections and an enlarged bibliography. The list of open questions has beenupdated comments and references have been added about those previously openproblems that have been solved after the first edition appeared. TOCInverseand Direct Limits. Profinite Groups. Free Profinite Groups. Some SpecialProfinite Groups. Discrete and Profinite Modules. Homology and Cohomology ofProfinite Groups. Cohomological Dimension. Normal Subgroups of Free ProC Groups. Free Constructions. Open Questions. Appendices AD Bibliography Indices. «