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Profinite graphs and groups [electronic resource]

Profinite graphs and groups [electronic resource]

Material type
E-Book(소장)
Personal Author
Ribes, Luis.
Title Statement
Profinite graphs and groups [electronic resource] / Luis Ribes.
Publication, Distribution, etc
Cham :   Springer,   c2017.  
Physical Medium
1 online resource. (xv, 471 p.).
Series Statement
Ergebnisse der Mathematik und ihrer Grenzgebiete. A series of modern surveys in mathematics,0071-1136 ; 3. Folge, 66
ISBN
9783319610412 9783319611990 (eBook)
요약
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.
General Note
Title from e-Book title page.  
Content Notes
1 Preliminaries -- Part I Basic Theory -- 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 -- Part II Applications to Profinite 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 -- Part III Applications to Abstract Groups -- 11 Separability Conditions in Free and Polycyclic Groups -- 12 Algorithms in 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 Amalgamated Products -- Appendix A Abstract Graphs -- Appendix B Rational Sets in Free Groups and Automata -- Bibliography -- Index.
Bibliography, Etc. Note
Includes bibliographical references and indexes.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Topological Groups. Group theory.
Short cut
URL
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001 000045987608
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006 m d
007 cr
008 190624s2017 sz ob 001 0 eng d
020 ▼a 9783319610412
020 ▼a 9783319611990 (eBook)
040 ▼a 211009 ▼c 211009 ▼d 211009
050 4 ▼a QA252.3
082 0 4 ▼a 512.55 ▼2 23
084 ▼a 512.55 ▼2 DDCK
090 ▼a 512.55
100 1 ▼a Ribes, Luis.
245 1 0 ▼a Profinite graphs and groups ▼h [electronic resource] / ▼c Luis Ribes.
260 ▼a Cham : ▼b Springer, ▼c c2017.
300 ▼a 1 online resource. (xv, 471 p.).
490 1 ▼a Ergebnisse der Mathematik und ihrer Grenzgebiete. A series of modern surveys in mathematics, ▼x 0071-1136 ; ▼v 3. Folge, 66
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and indexes.
505 0 ▼a 1 Preliminaries -- Part I Basic Theory -- 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 -- Part II Applications to Profinite 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 -- Part III Applications to Abstract Groups -- 11 Separability Conditions in Free and Polycyclic Groups -- 12 Algorithms in 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 Amalgamated Products -- Appendix A Abstract Graphs -- Appendix B Rational Sets in Free Groups and Automata -- Bibliography -- Index.
520 ▼a 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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Topological Groups.
650 0 ▼a Group theory.
830 0 ▼a Ergebnisse der Mathematik und ihrer Grenzgebiete. ▼p Series of modern surveys in mathematics, ▼x 0071-1136 ; ▼v 3. Folge, 66.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=https://doi.org/10.1007/978-3-319-61199-0
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

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No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.55 Accession No. E14013862 Availability Loan can not(reference room) Due Date Make a Reservation Service M

Contents information

Table of Contents

1 Preliminaries -- Part I Basic Theory -- 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 -- Part II Applications to Profinite 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 -- Part III Applications to Abstract Groups -- 11 Separability Conditions in Free and Polycyclic Groups -- 12 Algorithms in 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 Amalgamated Products -- Appendix A Abstract Graphs -- Appendix B Rational Sets in Free Groups and Automata -- Bibliography -- Index.

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