Generators and Relations for Discrete Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1957
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik"
14 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | When we began to consider the scope of this book, we envisaged a catalogue supplying at least one abstract definition for any finitely generated group that the reader might propose. But we soon realized that more or less arbitrary restrictions are necessary, because interesting groups are so numerous. For permutation groups of degree 8 or less (i. e., subgroups of e ), the reader cannot do better than consult the 8 tables of JosEPHINE BuRNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134-143) deal with groups of low order, finiteandinfinite groups of congruent transformations, symmetric and alternating groups, linear fractional groups, and groups generated by reflections in real Euclidean space of any number of dimensions. The best substitute foramoreextensive catalogue is the description (in Chapter 2) of a method whereby the reader can easily work out his own abstract definition for almost any given finite group. This method is sufficiently mechanical for the use of an electronic computer. There is also a topological method (Chapter 3), suitable not only for groups of low order but also for some infinite groups. This involves choosing a set of generators, constructing a certain graph (the Cayley diagram or DEHNsehe Gruppenbild), and embedding the graph into a surface. Cases in which the surface is a sphere or a plane are described in Chapter 4, where we obtain algebraically, and verify topologically, an abstract definition for each of the 17 space groups of two-dimensional crystallography |
| Beschreibung: | 1 Online-Ressource (VIII, 155 p) |
| ISBN: | 9783662257395 9783662236543 |
| DOI: | 10.1007/978-3-662-25739-5 |
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| 490 | 0 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" |v 14 | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Coxeter, H. S. M. |
| author_facet | Coxeter, H. S. M. |
| author_role | aut |
| author_sort | Coxeter, H. S. M. |
| author_variant | h s m c hsm hsmc |
| building | Verbundindex |
| bvnumber | BV042423520 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)858995243 (DE-599)BVBBV042423520 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-25739-5 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662257395 9783662236543 |
| language | English |
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| spelling | Coxeter, H. S. M. Verfasser aut Generators and Relations for Discrete Groups by H. S. M. Coxeter, W. O. J. Moser Berlin, Heidelberg Springer Berlin Heidelberg 1957 1 Online-Ressource (VIII, 155 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" 14 When we began to consider the scope of this book, we envisaged a catalogue supplying at least one abstract definition for any finitely generated group that the reader might propose. But we soon realized that more or less arbitrary restrictions are necessary, because interesting groups are so numerous. For permutation groups of degree 8 or less (i. e., subgroups of e ), the reader cannot do better than consult the 8 tables of JosEPHINE BuRNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134-143) deal with groups of low order, finiteandinfinite groups of congruent transformations, symmetric and alternating groups, linear fractional groups, and groups generated by reflections in real Euclidean space of any number of dimensions. The best substitute foramoreextensive catalogue is the description (in Chapter 2) of a method whereby the reader can easily work out his own abstract definition for almost any given finite group. This method is sufficiently mechanical for the use of an electronic computer. There is also a topological method (Chapter 3), suitable not only for groups of low order but also for some infinite groups. This involves choosing a set of generators, constructing a certain graph (the Cayley diagram or DEHNsehe Gruppenbild), and embedding the graph into a surface. Cases in which the surface is a sphere or a plane are described in Chapter 4, where we obtain algebraically, and verify topologically, an abstract definition for each of the 17 space groups of two-dimensional crystallography Mathematics Algebra Mathematik Erzeugende (DE-588)4152978-9 gnd rswk-swf Relation Mathematik (DE-588)4177675-6 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Erzeugendensystem (DE-588)4201996-5 gnd rswk-swf Erzeugendes Element (DE-588)4413601-8 gnd rswk-swf Diskrete Gruppe (DE-588)4135541-6 gnd rswk-swf Generator (DE-588)4020119-3 gnd rswk-swf Diskrete Gruppe (DE-588)4135541-6 s Erzeugende (DE-588)4152978-9 s Relation Mathematik (DE-588)4177675-6 s 1\p DE-604 Erzeugendensystem (DE-588)4201996-5 s 2\p DE-604 Erzeugendes Element (DE-588)4413601-8 s 3\p DE-604 Generator (DE-588)4020119-3 s 4\p DE-604 Gruppentheorie (DE-588)4072157-7 s 5\p DE-604 Moser, W. O. J. Sonstige oth https://doi.org/10.1007/978-3-662-25739-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Coxeter, H. S. M. Generators and Relations for Discrete Groups Mathematics Algebra Mathematik Erzeugende (DE-588)4152978-9 gnd Relation Mathematik (DE-588)4177675-6 gnd Gruppentheorie (DE-588)4072157-7 gnd Erzeugendensystem (DE-588)4201996-5 gnd Erzeugendes Element (DE-588)4413601-8 gnd Diskrete Gruppe (DE-588)4135541-6 gnd Generator (DE-588)4020119-3 gnd |
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| title | Generators and Relations for Discrete Groups |
| title_auth | Generators and Relations for Discrete Groups |
| title_exact_search | Generators and Relations for Discrete Groups |
| title_full | Generators and Relations for Discrete Groups by H. S. M. Coxeter, W. O. J. Moser |
| title_fullStr | Generators and Relations for Discrete Groups by H. S. M. Coxeter, W. O. J. Moser |
| title_full_unstemmed | Generators and Relations for Discrete Groups by H. S. M. Coxeter, W. O. J. Moser |
| title_short | Generators and Relations for Discrete Groups |
| title_sort | generators and relations for discrete groups |
| topic | Mathematics Algebra Mathematik Erzeugende (DE-588)4152978-9 gnd Relation Mathematik (DE-588)4177675-6 gnd Gruppentheorie (DE-588)4072157-7 gnd Erzeugendensystem (DE-588)4201996-5 gnd Erzeugendes Element (DE-588)4413601-8 gnd Diskrete Gruppe (DE-588)4135541-6 gnd Generator (DE-588)4020119-3 gnd |
| topic_facet | Mathematics Algebra Mathematik Erzeugende Relation Mathematik Gruppentheorie Erzeugendensystem Erzeugendes Element Diskrete Gruppe Generator |
| url | https://doi.org/10.1007/978-3-662-25739-5 |
| work_keys_str_mv | AT coxeterhsm generatorsandrelationsfordiscretegroups AT moserwoj generatorsandrelationsfordiscretegroups |