Groups, graphs and trees :: an introduction to the geometry of infinite groups /
Presenting groups in a formal, abstract algebraic manner is both useful and powerful, yet it avoids a fascinating geometric perspective on group theory - which is also useful and powerful, particularly in the study of infinite groups. This book presents the modern, geometric approach to group theory...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK ; New York :
Cambridge University Press,
2008.
|
| Schriftenreihe: | London Mathematical Society student texts ;
73. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Presenting groups in a formal, abstract algebraic manner is both useful and powerful, yet it avoids a fascinating geometric perspective on group theory - which is also useful and powerful, particularly in the study of infinite groups. This book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory. |
| Beschreibung: | 1 online resource (xi, 231 pages) |
| Bibliographie: | Includes bibliographical references (pages 227-229) and index. |
| ISBN: | 9780511424427 0511424426 0511423942 9780511423949 9780521895453 0521895456 9780521719773 0521719771 0511422792 9780511422799 9781139167505 1139167502 1107201527 9781107201521 1281791210 9781281791214 9786611791216 6611791213 0511423454 9780511423451 |
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| 504 | |a Includes bibliographical references (pages 227-229) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preface -- Cayley's theorems -- Groups generated by reflections -- Groups acting on trees -- Baumslag-Solitar groups -- Words and Dehn's word problem -- A finitely-generated, infinite, Torsion group -- Regular languages and normal forms -- The Lamplighter group -- The geometry of infinite groups -- Thompson's group -- The large-scale geometry of groups. | |
| 520 | |a Presenting groups in a formal, abstract algebraic manner is both useful and powerful, yet it avoids a fascinating geometric perspective on group theory - which is also useful and powerful, particularly in the study of infinite groups. This book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory. | ||
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| contents | Preface -- Cayley's theorems -- Groups generated by reflections -- Groups acting on trees -- Baumslag-Solitar groups -- Words and Dehn's word problem -- A finitely-generated, infinite, Torsion group -- Regular languages and normal forms -- The Lamplighter group -- The geometry of infinite groups -- Thompson's group -- The large-scale geometry of groups. |
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| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| genre_facet | Electronic book. Electronic books. |
| id | ZDB-4-EBA-ocn276371021 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:34Z |
| institution | BVB |
| isbn | 9780511424427 0511424426 0511423942 9780511423949 9780521895453 0521895456 9780521719773 0521719771 0511422792 9780511422799 9781139167505 1139167502 1107201527 9781107201521 1281791210 9781281791214 9786611791216 6611791213 0511423454 9780511423451 |
| language | English |
| oclc_num | 276371021 |
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| physical | 1 online resource (xi, 231 pages) |
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| publisher | Cambridge University Press, |
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| series | London Mathematical Society student texts ; |
| series2 | London Mathematical Society student texts ; |
| spelling | Meier, John, 1965- https://id.oclc.org/worldcat/entity/E39PCjwhvVkb8RMf37q3p6TH3P http://id.loc.gov/authorities/names/n2008019909 Groups, graphs and trees : an introduction to the geometry of infinite groups / John Meier. Cambridge, UK ; New York : Cambridge University Press, 2008. 1 online resource (xi, 231 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file London Mathematical Society student texts ; 73 Includes bibliographical references (pages 227-229) and index. Print version record. Preface -- Cayley's theorems -- Groups generated by reflections -- Groups acting on trees -- Baumslag-Solitar groups -- Words and Dehn's word problem -- A finitely-generated, infinite, Torsion group -- Regular languages and normal forms -- The Lamplighter group -- The geometry of infinite groups -- Thompson's group -- The large-scale geometry of groups. Presenting groups in a formal, abstract algebraic manner is both useful and powerful, yet it avoids a fascinating geometric perspective on group theory - which is also useful and powerful, particularly in the study of infinite groups. This book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory. English. Infinite groups. http://id.loc.gov/authorities/subjects/sh85066100 Groupes infinis. MATHEMATICS Group Theory. bisacsh Infinite groups fast Unendliche Gruppe gnd http://d-nb.info/gnd/4375539-2 Geometrische Gruppentheorie gnd http://d-nb.info/gnd/4651615-3 Electronic book. Electronic books. has work: Groups, graphs and trees (Text) https://id.oclc.org/worldcat/entity/E39PCH8KKx469mkDGbcCXcH8JC https://id.oclc.org/worldcat/ontology/hasWork Print version: Meier, John, 1965- Groups, graphs and trees. Cambridge, UK ; New York : Cambridge University Press, 2008 9780521895453 0521895456 (DLC) 2008012848 (OCoLC)213495461 London Mathematical Society student texts ; 73. http://id.loc.gov/authorities/names/n84727069 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=244539 Volltext |
| spellingShingle | Meier, John, 1965- Groups, graphs and trees : an introduction to the geometry of infinite groups / London Mathematical Society student texts ; Preface -- Cayley's theorems -- Groups generated by reflections -- Groups acting on trees -- Baumslag-Solitar groups -- Words and Dehn's word problem -- A finitely-generated, infinite, Torsion group -- Regular languages and normal forms -- The Lamplighter group -- The geometry of infinite groups -- Thompson's group -- The large-scale geometry of groups. Infinite groups. http://id.loc.gov/authorities/subjects/sh85066100 Groupes infinis. MATHEMATICS Group Theory. bisacsh Infinite groups fast Unendliche Gruppe gnd http://d-nb.info/gnd/4375539-2 Geometrische Gruppentheorie gnd http://d-nb.info/gnd/4651615-3 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85066100 http://d-nb.info/gnd/4375539-2 http://d-nb.info/gnd/4651615-3 |
| title | Groups, graphs and trees : an introduction to the geometry of infinite groups / |
| title_auth | Groups, graphs and trees : an introduction to the geometry of infinite groups / |
| title_exact_search | Groups, graphs and trees : an introduction to the geometry of infinite groups / |
| title_full | Groups, graphs and trees : an introduction to the geometry of infinite groups / John Meier. |
| title_fullStr | Groups, graphs and trees : an introduction to the geometry of infinite groups / John Meier. |
| title_full_unstemmed | Groups, graphs and trees : an introduction to the geometry of infinite groups / John Meier. |
| title_short | Groups, graphs and trees : |
| title_sort | groups graphs and trees an introduction to the geometry of infinite groups |
| title_sub | an introduction to the geometry of infinite groups / |
| topic | Infinite groups. http://id.loc.gov/authorities/subjects/sh85066100 Groupes infinis. MATHEMATICS Group Theory. bisacsh Infinite groups fast Unendliche Gruppe gnd http://d-nb.info/gnd/4375539-2 Geometrische Gruppentheorie gnd http://d-nb.info/gnd/4651615-3 |
| topic_facet | Infinite groups. Groupes infinis. MATHEMATICS Group Theory. Infinite groups Unendliche Gruppe Geometrische Gruppentheorie Electronic book. Electronic books. |
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| work_keys_str_mv | AT meierjohn groupsgraphsandtreesanintroductiontothegeometryofinfinitegroups |