Verfügbarkeit: Generators and relations for discrete groups

Generators and relations for discrete groups:

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Bibliographische Detailangaben
Beteiligte Personen:	Coxeter, Harold S. M. 1907-2003 (VerfasserIn), Moser, W. O. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 1972
Ausgabe:	3. ed.
Schriftenreihe:	Ergebnisse der Mathematik und ihrer Grenzgebiete 14
Schlagwörter:	Discrete groepen Discrete groups Group theory > Generators Group theory > Relations Diskrete Gruppe Erzeugende Erzeugendes Element Generator Erzeugendensystem Gruppentheorie Relation > Mathematik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001909401&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	IX, 161 S. graph. Darst.
ISBN:	3540058370 0387058370

Internformat

MARC


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Datensatz im Suchindex

DE-BY-TUM_call_number	0102 MAT 200f 2001 A 9859(3)
DE-BY-TUM_katkey	488369
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adam_text	Contents 1. Cyclic, Dicyclic and Metacyclic Groups 1 1.1 Generators and relations 1 1.2 Factor groups 2 1.3 Direct products 3 1.4 Automorphisms 5 1.5 Some well-known finite groups 6 1.6 Dicyclic groups 7 1.7 The quaternion group 8 1.8 Cyclic extensions of cyclic groups 9 1.9 Groups of order less than 32 11 2. Systematic Enumeration of Cosets 12 2.1 Finding an abstract definition for a finite group 12 2.2 Examples 14 2.3 The corresponding permutations 17 2.4 Finding whether a given subgroup is normal 17 2.5 How an abstract definition determines a group 18 3. Graphs, Maps and Cayley Diagrams 18 3.1 Graphs 19 3.2 Maps 20 3.3 Cayley diagrams 21 3.4 Planar diagrams 23 3.5 Unbounded surfaces 24 3.6 Non-planar diagrams 28 3.7 Schreier s coset diagrams 31 4. Abstract Crystallography 32 4.1 The cyclic and dihedral groups 33 4.2 The crystallographic and non-crystallographic point groups . . 33 4.3 Groups generated by reflections 35 4.4 Subgroups of the reflection groups 38 4.5 The seventeen two-dimensional space groups 40 4.6 Subgroup relationships among the seventeen groups 51 5. Hyperbolic Tessellations and Fundamental Groups 52 5.1 Regular tessellations 52 5.2 The Petrie polygon 53 5.3 Dyck s groups 54 5.4 The fundamental group for a non-orientable surface, obtained as a group generated by glide-reflections 56 5.5 The fundamental group for an orientable surface, obtained as a group of translations 58 Contents IX 6. The Symmetric, Alternating, and other Special Groups 61 6.1 Artin s braid group 62 6.2 The symmetric group 63 6.3 The alternating group 66 6.4 The polyhedral groups 67 6.5 The binary polyhedral groups 68 6.6 Miller s generalization of the polyhedral groups 71 6.7 A new generalization 76 6.8 Burnside s problem 80 7. Modular and Linear Fractional Groups 83 7.1 Lattices and modular groups 83 7.2 Defining relations when n = 2 85 7.3 Defining relations when n 2: 3 88 7.4 Linear fractional groups 92 7.5 The case when n = 2 and q = p, a prime 93 7.6 The groups LF(2, 2m) 97 7.7 The Hessian group and LF(3, 3) 98 7.8 The Mathieu groups 99 8. Regular Maps 101 8.1 Automorphisms 101 8.2 Universal covering 103 8.3 Maps of type {4, 4} on a torus 103 8.4 Maps of type {3, 6} or {6, 3} on a torus 107 8.5 Maps having specified holes 109 8.6 Maps having specified Petrie polygons 111 8.7 Maps having two faces 113 8.8 Maps on a two-sheeted Riemann surface 115 8.9 Symmetrical graphs 117 9. Groups Generated by Reflections 117 9.1 Reducible and irreducible groups 117 9.2 The graphical notation 118 9.3 Finite groups 119 9.4 A brief description of the individual groups 123 9.5 Commutator subgroups 124 9.6 Central quotient groups 127 9.7 Exponents and invariants 129 9.8 Infinite Euclidean groups 131 9.9 Infinite non-Euclidean groups 132 Tables 1-12 134 Bibliography 143 Index 157
any_adam_object	1
author	Coxeter, Harold S. M. 1907-2003 Moser, W. O.
author_GND	(DE-588)118522507
author_facet	Coxeter, Harold S. M. 1907-2003 Moser, W. O.
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discipline	Mathematik
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id	DE-604.BV003047727
illustrated	Illustrated
indexdate	2024-12-20T07:57:57Z
institution	BVB
isbn	3540058370 0387058370
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-001909401
oclc_num	402507
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owner_facet	DE-384 DE-91G DE-BY-TUM DE-29T DE-703 DE-19 DE-BY-UBM DE-188
physical	IX, 161 S. graph. Darst.
publishDate	1972
publishDateSearch	1972
publishDateSort	1972
publisher	Springer
record_format	marc
series	Ergebnisse der Mathematik und ihrer Grenzgebiete
series2	Ergebnisse der Mathematik und ihrer Grenzgebiete
spellingShingle	Coxeter, Harold S. M. 1907-2003 Moser, W. O. Generators and relations for discrete groups Ergebnisse der Mathematik und ihrer Grenzgebiete Discrete groepen gtt Discrete groups Group theory Generators Group theory Relations Diskrete Gruppe (DE-588)4135541-6 gnd Erzeugende (DE-588)4152978-9 gnd Erzeugendes Element (DE-588)4413601-8 gnd Generator (DE-588)4020119-3 gnd Erzeugendensystem (DE-588)4201996-5 gnd Gruppentheorie (DE-588)4072157-7 gnd Relation Mathematik (DE-588)4177675-6 gnd
subject_GND	(DE-588)4135541-6 (DE-588)4152978-9 (DE-588)4413601-8 (DE-588)4020119-3 (DE-588)4201996-5 (DE-588)4072157-7 (DE-588)4177675-6
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 H. S. M. Coxeter ; W. O. J. Moser
title_fullStr	Generators and relations for discrete groups H. S. M. Coxeter ; W. O. J. Moser
title_full_unstemmed	Generators and relations for discrete groups 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	Discrete groepen gtt Discrete groups Group theory Generators Group theory Relations Diskrete Gruppe (DE-588)4135541-6 gnd Erzeugende (DE-588)4152978-9 gnd Erzeugendes Element (DE-588)4413601-8 gnd Generator (DE-588)4020119-3 gnd Erzeugendensystem (DE-588)4201996-5 gnd Gruppentheorie (DE-588)4072157-7 gnd Relation Mathematik (DE-588)4177675-6 gnd
topic_facet	Discrete groepen Discrete groups Group theory Generators Group theory Relations Diskrete Gruppe Erzeugende Erzeugendes Element Generator Erzeugendensystem Gruppentheorie Relation Mathematik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001909401&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV005871160
work_keys_str_mv	AT coxeterharoldsm generatorsandrelationsfordiscretegroups AT moserwo generatorsandrelationsfordiscretegroups

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