Profinite graphs and groups / Luis Ribes.
Material type:
TextSeries: Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / a series of modern surveys in mathematics ; v 66.Publication details: Cham : Springer, 2017.Description: xv, 471 pages : illustrations ; 25 cmISBN: - 9783319610412 (hardcover : alk. paper)
- 512.2 23 R485
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 512.2 R485 (Browse shelf(Opens below)) | Available | 138281 |
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| 512.2 R367 Selected works | 512.2 R432 Finite simple groups | 512.2 R476 Applications of automata theory and algebra | 512.2 R485 Profinite graphs and groups / | 512.2 R643 Local newforms for GSp(4) | 512.2 R659 Finiteness conditions and generalized soluble groups | 512.2 R659 Finiteness conditions and generalized soluble groups |
Include bibliographical references and indexes.
1. Preliminaries --
2. Profinite graphs --
3. The fundamental group of a profinite graph --
4. Profinite groups acting on C-trees --
5. Free products of pro-C groups --
6. Graphs of pro-C groups --
7. Subgroups of fundamental groups of graphs of groups --
8. Minimal subtrees --
9. Homology and graphs of pro-C groups --
10. The virtual cohomological dimension of profinite groups --
11. Separability conditions in free and polycyclic groups --
12. Algorithms in abstract free groups and monoids --
13. Abstract groups vs their profinite completions --
14. Conjugacy in free products and in free-by-finite groups --
15. Conjugacy separability in amalgated products --
Appendix A. Abstract graphs --
Appendix B. Rational sets in free groups and automata.
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open questions and suggestions for further reading.
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