LEADER 04124nam 22006015 450 001 9910254298703321 005 20200703171501.0 010 $a3-319-61199-2 024 7 $a10.1007/978-3-319-61199-0 035 $a(CKB)3710000001631062 035 $a(DE-He213)978-3-319-61199-0 035 $a(MiAaPQ)EBC4984498 035 $a(PPN)20385070X 035 $a(EXLCZ)993710000001631062 100 $a20170823d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aProfinite Graphs and Groups /$fby Luis Ribes 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XV, 471 p.) 225 1 $aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v66 311 $a3-319-61041-4 320 $aIncludes bibliographical references and indexes. 327 $a1 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. 330 $aThis book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open questions and suggestions for further reading. 410 0$aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v66 606 $aTopological groups 606 $aLie groups 606 $aGraph theory 606 $aGroup theory 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 615 0$aTopological groups. 615 0$aLie groups. 615 0$aGraph theory. 615 0$aGroup theory. 615 14$aTopological Groups, Lie Groups. 615 24$aGraph Theory. 615 24$aGroup Theory and Generalizations. 676 $a512.2 700 $aRibes$b Luis$4aut$4http://id.loc.gov/vocabulary/relators/aut$062677 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254298703321 996 $aProfinite graphs and groups$91560437 997 $aUNINA