Generators and relations for discrete groups:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1972
|
| Edition: | 3. ed. |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
14 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 161 S. graph. Darst. |
| ISBN: | 3540058370 0387058370 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804117336363368448 |
|---|---|
| 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. |
| author_role | aut aut |
| author_sort | Coxeter, Harold S. M. 1907-2003 |
| author_variant | h s m c hsm hsmc w o m wo wom |
| building | Verbundindex |
| bvnumber | BV003047727 |
| callnumber-first | Q - Science |
| callnumber-label | QA171 |
| callnumber-raw | QA171 |
| callnumber-search | QA171 |
| callnumber-sort | QA 3171 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)402507 (DE-599)BVBBV003047727 |
| 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 |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV003047727 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:52:47Z |
| 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 | DE-384 DE-91G DE-BY-TUM DE-29T DE-703 DE-19 DE-BY-UBM DE-188 |
| 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 |
| spelling | Coxeter, Harold S. M. 1907-2003 Verfasser (DE-588)118522507 aut Generators and relations for discrete groups H. S. M. Coxeter ; W. O. J. Moser 3. ed. Berlin [u.a.] Springer 1972 IX, 161 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 14 Discrete groepen gtt Discrete groups Group theory Generators Group theory Relations Diskrete Gruppe (DE-588)4135541-6 gnd rswk-swf Erzeugende (DE-588)4152978-9 gnd rswk-swf Erzeugendes Element (DE-588)4413601-8 gnd rswk-swf Generator (DE-588)4020119-3 gnd rswk-swf Erzeugendensystem (DE-588)4201996-5 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Relation Mathematik (DE-588)4177675-6 gnd rswk-swf Diskrete Gruppe (DE-588)4135541-6 s Erzeugende (DE-588)4152978-9 s Relation Mathematik (DE-588)4177675-6 s DE-604 Gruppentheorie (DE-588)4072157-7 s Generator (DE-588)4020119-3 s Erzeugendensystem (DE-588)4201996-5 s 1\p DE-604 Erzeugendes Element (DE-588)4413601-8 s 2\p DE-604 Moser, W. O. Verfasser aut Ergebnisse der Mathematik und ihrer Grenzgebiete 14 (DE-604)BV005871160 14 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis 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 |
| 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 |