The history of combinatorial group theory: a case study in the history of ideas
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1982
|
| Schriftenreihe: | Studies in the history of mathematics and physical sciences
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 234 S. |
| ISBN: | 0387907491 3540907491 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804114691705798656 |
|---|---|
| adam_text | Table of Contents
Part I The Beginning of Combinatorial Group Theory
1.1 Introduction to Part I 3
1.2 The Foundations: Dyck s Group Theoretical Studies 5
1.3 The Origin: The Theory of Discontinuous Groups 11
1.4 Motivation: The Fundamental Groups of Topological Spaces 14
1.5 The Graphical Representation of Groups 22
1.6 Precursors of Later Developments 29
A. Arithmetically Defined Linear Groups in
Higher Dimensions 30
B. Arithmetically Defined Linear Groups in
Two Dimensions 34
C. Geometric Constructions. Fuchsian Groups 38
D. Braid Groups and Mapping Class Groups 39
E. Differential Equations, Linear Groups, and Lie Groups 40
F. Finite Groups 44
1.7 Summary 51
1.8 Modes of Communication. Growth and
Distribution of Research in Group Theory 58
1.9 Biographical Notes 68
1.10 Notes on Terminology and Definitions 71
I.I 1 Sources 75
Part II The Emergence of Combinatorial Group Theory
as an Independent Field
II. 1 Introduction to Part II 79
11.2 Free Groups and Their Automorphisms 81
11.3 The Reidemeister Schreier Method 91
viii Contents
11.4 Free Products and Free Products with Amalgamations 102
11.5 One Relator Groups 113
11.6 Metabelian Groups and Related Topics 122
A. The Principal Ideal Theorem 124
B. Applications to the Theory of Knots and Links 134
C. A Problem from the Foundations of Geometry 136
D. Notes on Later Developments and Generalizations 138
11.7 Commutator Calculus and the Lower Central Series 141
11.8 Varieties of Groups 157
11.9 Topological Properties of Groups and Group Extensions 162
11.10 Notes on Special Groups 175
II. 11 Postscript: The Impact of Mathematical Logic 181
11.12 Modes of Communication 187
11.13 Geographical Distribution of Research and Effects of Migration 193
11.14 Organization of Knowledge 200
Bibliography 207
Index of Names 227
Index of Subjects 231
|
| any_adam_object | 1 |
| author | Chandler, Bruce Magnus, Wilhelm 1907-1990 |
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| dewey-full | 512/.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.22 |
| dewey-search | 512/.22 |
| dewey-sort | 3512 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000228685 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:10:45Z |
| institution | BVB |
| isbn | 0387907491 3540907491 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000136947 |
| oclc_num | 8627057 |
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| physical | VIII, 234 S. |
| psigel | TUB-nveb HUB-WG055nak200601 |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Springer |
| record_format | marc |
| series | Studies in the history of mathematics and physical sciences |
| series2 | Studies in the history of mathematics and physical sciences |
| spelling | Chandler, Bruce Verfasser aut The history of combinatorial group theory a case study in the history of ideas Bruce Chandler ; Wilhelm Magnus New York [u.a.] Springer 1982 VIII, 234 S. txt rdacontent n rdamedia nc rdacarrier Studies in the history of mathematics and physical sciences 9 Analyse combinatoire, Histoire Combinatieleer gtt Groepentheorie gtt Groupes (Théorie des), Histoire Groupes, Théorie combinatoire des Geschichte Combinatorial group theory History Geschichte (DE-588)4020517-4 gnd rswk-swf Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Kombinatorische Gruppentheorie (DE-588)4219556-1 s Geschichte (DE-588)4020517-4 s DE-604 Gruppentheorie (DE-588)4072157-7 s Magnus, Wilhelm 1907-1990 Verfasser (DE-588)119325721 aut Studies in the history of mathematics and physical sciences 9 (DE-604)BV000003995 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000136947&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chandler, Bruce Magnus, Wilhelm 1907-1990 The history of combinatorial group theory a case study in the history of ideas Studies in the history of mathematics and physical sciences Analyse combinatoire, Histoire Combinatieleer gtt Groepentheorie gtt Groupes (Théorie des), Histoire Groupes, Théorie combinatoire des Geschichte Combinatorial group theory History Geschichte (DE-588)4020517-4 gnd Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4020517-4 (DE-588)4219556-1 (DE-588)4072157-7 |
| title | The history of combinatorial group theory a case study in the history of ideas |
| title_auth | The history of combinatorial group theory a case study in the history of ideas |
| title_exact_search | The history of combinatorial group theory a case study in the history of ideas |
| title_full | The history of combinatorial group theory a case study in the history of ideas Bruce Chandler ; Wilhelm Magnus |
| title_fullStr | The history of combinatorial group theory a case study in the history of ideas Bruce Chandler ; Wilhelm Magnus |
| title_full_unstemmed | The history of combinatorial group theory a case study in the history of ideas Bruce Chandler ; Wilhelm Magnus |
| title_short | The history of combinatorial group theory |
| title_sort | the history of combinatorial group theory a case study in the history of ideas |
| title_sub | a case study in the history of ideas |
| topic | Analyse combinatoire, Histoire Combinatieleer gtt Groepentheorie gtt Groupes (Théorie des), Histoire Groupes, Théorie combinatoire des Geschichte Combinatorial group theory History Geschichte (DE-588)4020517-4 gnd Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Analyse combinatoire, Histoire Combinatieleer Groepentheorie Groupes (Théorie des), Histoire Groupes, Théorie combinatoire des Geschichte Combinatorial group theory History Kombinatorische Gruppentheorie Gruppentheorie |
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| volume_link | (DE-604)BV000003995 |
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