Topics in the theory of group presentations /:
These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of Nottingham. Many new examples and exercises ha...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [England] ; New York :
Cambridge University Press,
1980.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
42. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of Nottingham. Many new examples and exercises have been added and the treatment of a number of topics has been improved and expanded. In addition, there are new chapters on the triangle groups, small cancellation theory and groups from topology. The connections between the theory of group presentations and other areas of mathematics are emphasized throughout. The book can be used as a text for beginning research students and, for specialists in other fields, serves as an introduction both to the subject and to more advanced treatises. |
| Beschreibung: | 1 online resource (vii, 311 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and indexes. |
| ISBN: | 9781107360945 1107360943 9780511629303 0511629303 |
| ISSN: | 0076-0552 |
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| 505 | 0 | |a Cover; Title; Copyright; Contents; Preface; Chapter I. Free groups and free presentations; 1. Elementary properties of free groups; 2. The Nielsen-Schreier theorem; 3. Free presentations of groups; 4. Elementary properties of presentations; Chapter II. Examples of presentations; 5. Some popular groups; 6. Finitely-generated abelian groups; Chapter III. Groups with few relations; 7. Metacyclic groups; 8. Interesting groups with three generators; 9. Cyclically-presented groups; Chapter IV. Presentations of subgroups; 10. A special case; 11. Coset enumeration | |
| 505 | 8 | |a 12. The Reidemeister-Schreier rewriting process13. A method for presenting subgroups; Chapter V. The triangle groups; 14. The Euclidian case; 15. The elliptic case; 16. The hyperbolic case; Chapter VI. Extensions of groups; 17. Extension theory; 18. Teach yourself cohomology of groups; 19. Local cohomology and p-groups; 20. Presentations of group extensions; 21. The Golod-Safarevic theorem; 22. Some minimal presentations; Chapter VII. Small cancellation groups; 23. van Kampen diagrams; 24. From Eulerfs formula to Dehn's algorithm; 25. The existence of non-cyclic free subgroups | |
| 505 | 8 | |a 26. Some infinite Fibonacci groupsChapter VIII. Groups from topology; 27. Surfaces; 28. Knots; 29. Braids; 30. Tangles; Guide to the literature and references; Index of notation; Index | |
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| contents | Cover; Title; Copyright; Contents; Preface; Chapter I. Free groups and free presentations; 1. Elementary properties of free groups; 2. The Nielsen-Schreier theorem; 3. Free presentations of groups; 4. Elementary properties of presentations; Chapter II. Examples of presentations; 5. Some popular groups; 6. Finitely-generated abelian groups; Chapter III. Groups with few relations; 7. Metacyclic groups; 8. Interesting groups with three generators; 9. Cyclically-presented groups; Chapter IV. Presentations of subgroups; 10. A special case; 11. Coset enumeration 12. The Reidemeister-Schreier rewriting process13. A method for presenting subgroups; Chapter V. The triangle groups; 14. The Euclidian case; 15. The elliptic case; 16. The hyperbolic case; Chapter VI. Extensions of groups; 17. Extension theory; 18. Teach yourself cohomology of groups; 19. Local cohomology and p-groups; 20. Presentations of group extensions; 21. The Golod-Safarevic theorem; 22. Some minimal presentations; Chapter VII. Small cancellation groups; 23. van Kampen diagrams; 24. From Eulerfs formula to Dehn's algorithm; 25. The existence of non-cyclic free subgroups 26. Some infinite Fibonacci groupsChapter VIII. Groups from topology; 27. Surfaces; 28. Knots; 29. Braids; 30. Tangles; Guide to the literature and references; Index of notation; Index |
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| spelling | Johnson, D. L. Topics in the theory of group presentations / D.L. Johnson. Cambridge [England] ; New York : Cambridge University Press, 1980. 1 online resource (vii, 311 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 42, 0076-0552 Includes bibliographical references and indexes. Print version record. These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of Nottingham. Many new examples and exercises have been added and the treatment of a number of topics has been improved and expanded. In addition, there are new chapters on the triangle groups, small cancellation theory and groups from topology. The connections between the theory of group presentations and other areas of mathematics are emphasized throughout. The book can be used as a text for beginning research students and, for specialists in other fields, serves as an introduction both to the subject and to more advanced treatises. Cover; Title; Copyright; Contents; Preface; Chapter I. Free groups and free presentations; 1. Elementary properties of free groups; 2. The Nielsen-Schreier theorem; 3. Free presentations of groups; 4. Elementary properties of presentations; Chapter II. Examples of presentations; 5. Some popular groups; 6. Finitely-generated abelian groups; Chapter III. Groups with few relations; 7. Metacyclic groups; 8. Interesting groups with three generators; 9. Cyclically-presented groups; Chapter IV. Presentations of subgroups; 10. A special case; 11. Coset enumeration 12. The Reidemeister-Schreier rewriting process13. A method for presenting subgroups; Chapter V. The triangle groups; 14. The Euclidian case; 15. The elliptic case; 16. The hyperbolic case; Chapter VI. Extensions of groups; 17. Extension theory; 18. Teach yourself cohomology of groups; 19. Local cohomology and p-groups; 20. Presentations of group extensions; 21. The Golod-Safarevic theorem; 22. Some minimal presentations; Chapter VII. Small cancellation groups; 23. van Kampen diagrams; 24. From Eulerfs formula to Dehn's algorithm; 25. The existence of non-cyclic free subgroups 26. Some infinite Fibonacci groupsChapter VIII. Groups from topology; 27. Surfaces; 28. Knots; 29. Braids; 30. Tangles; Guide to the literature and references; Index of notation; Index Presentations of groups (Mathematics) http://id.loc.gov/authorities/subjects/sh85106447 Présentations de groupes (Mathématiques) MATHEMATICS Group Theory. bisacsh Presentations of groups (Mathematics) fast Gruppentheorie gnd Darstellungstheorie gnd http://d-nb.info/gnd/4148816-7 Print version: Johnson, D.L. Topics in the theory of group presentations. Cambridge [Eng.] ; New York : Cambridge University Press, 1980 0521231086 (DLC) 80040230 (OCoLC)6376214 London Mathematical Society lecture note series ; 42. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552427 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552427 Volltext |
| spellingShingle | Johnson, D. L. Topics in the theory of group presentations / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; Preface; Chapter I. Free groups and free presentations; 1. Elementary properties of free groups; 2. The Nielsen-Schreier theorem; 3. Free presentations of groups; 4. Elementary properties of presentations; Chapter II. Examples of presentations; 5. Some popular groups; 6. Finitely-generated abelian groups; Chapter III. Groups with few relations; 7. Metacyclic groups; 8. Interesting groups with three generators; 9. Cyclically-presented groups; Chapter IV. Presentations of subgroups; 10. A special case; 11. Coset enumeration 12. The Reidemeister-Schreier rewriting process13. A method for presenting subgroups; Chapter V. The triangle groups; 14. The Euclidian case; 15. The elliptic case; 16. The hyperbolic case; Chapter VI. Extensions of groups; 17. Extension theory; 18. Teach yourself cohomology of groups; 19. Local cohomology and p-groups; 20. Presentations of group extensions; 21. The Golod-Safarevic theorem; 22. Some minimal presentations; Chapter VII. Small cancellation groups; 23. van Kampen diagrams; 24. From Eulerfs formula to Dehn's algorithm; 25. The existence of non-cyclic free subgroups 26. Some infinite Fibonacci groupsChapter VIII. Groups from topology; 27. Surfaces; 28. Knots; 29. Braids; 30. Tangles; Guide to the literature and references; Index of notation; Index Presentations of groups (Mathematics) http://id.loc.gov/authorities/subjects/sh85106447 Présentations de groupes (Mathématiques) MATHEMATICS Group Theory. bisacsh Presentations of groups (Mathematics) fast Gruppentheorie gnd Darstellungstheorie gnd http://d-nb.info/gnd/4148816-7 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85106447 http://d-nb.info/gnd/4148816-7 |
| title | Topics in the theory of group presentations / |
| title_auth | Topics in the theory of group presentations / |
| title_exact_search | Topics in the theory of group presentations / |
| title_full | Topics in the theory of group presentations / D.L. Johnson. |
| title_fullStr | Topics in the theory of group presentations / D.L. Johnson. |
| title_full_unstemmed | Topics in the theory of group presentations / D.L. Johnson. |
| title_short | Topics in the theory of group presentations / |
| title_sort | topics in the theory of group presentations |
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| topic_facet | Presentations of groups (Mathematics) Présentations de groupes (Mathématiques) MATHEMATICS Group Theory. Gruppentheorie Darstellungstheorie |
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