Permutation groups and combinatorial structures:
Saved in:
| Previous Title: | Finite groups of automorphisms |
|---|---|
| Main Authors: | , |
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1979
|
| Series: | London Mathematical Society lecture note series
33 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 140 S. graph. Darst. |
| ISBN: | 0521222877 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804117958597804033 |
|---|---|
| adam_text | Contents
Page
Introduction vii
Note on the Projects viii
Chapter 1 Permutation Groups 1
1.1 Preliminary definitions 1
1.2 Counting principles 3
1.3 Transitivity 5
1. 4 Applications to group theory 9
1. 5 Extensions of multiply transitive groups 11
1.6 Primitivity 13
1. 7 Regular normal subgroups 17
1. 8 Project: Proof of Sylow s theorem 20
1.9 Project: Some multiply transitive groups 21
Notes and references 23
Chapter 2 Finite Geometries 24
2. 1 Introduction 24
2.2 Finite fields 26
2.3 Finite vector spaces 28
2.4 The structure of GL(V) and SL(V) 30
2. 5 Projective spaces and their groups 37
2. 6 More about projective spaces 41
2. 7 The classical simple groups 45
2. 8 Project: Near-fields and sharply 2-transitive groups 49
2.9 Project: Uniqueness of PG(2, 4) 51
2.10 Project: A unitary polarity in PG(2, 9) 51
Notes and references 52
Chapter 3 Designs 54
3.1 Four fundamental problems 54
3.2 Designs 55
3. 3 Symmetric designs 59
3.4 Automorphisms of designs 65
3.5 Extensions of designs 66
3. 6 Mathieu groups and associated designs 70
3. 7 Project: Hadamard matrices and designs 74
3. 8 Project: A 5 - (28, 7, 1) design 76
3. 9 Project: Uniqueness of the 3 - (22, 6, 1) design 76
Notes and references 78
Chapter 4 Groups and Graphs 80
4.1 Permutation groups and graphs 80
4.2 Automorphisms of graphs 85
4. 3 Rank 3 groups and the associated graphs 87
4. 4 Feasibility conditions for strongly regular graphs 89
4.5 The Higman-Sims group 93
4. 6 Project: Some graphs and their automorphism groups 99
4.7 Project: Strongly regular graphs and biplanes 100
Notes and references 101
Chapter 5 Maps 103
5.1 Maps and surfaces 103
5.2 Automorphisms of maps 109
5. 3 Cay ley graphs and Cay ley maps 115
5. 4 Complete maps and a theorem of Frobenius 122
5.5 Symmetrical maps 130
5.6 Project: Generalized Cayley maps 132
5. 7 Project: Paley maps 134
5.8 Project: Symmetrical Cayley maps 135
Notes and references 136
Index 138
|
| any_adam_object | 1 |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:02:40Z |
| institution | BVB |
| isbn | 0521222877 |
| language | English |
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| physical | 140 S. graph. Darst. |
| publishDate | 1979 |
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| publisher | Cambridge Univ. Press |
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| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | Biggs, Norman 1941- Verfasser (DE-588)136105580 aut Permutation groups and combinatorial structures N. L. Biggs ; A. T. White Cambridge [u.a.] Cambridge Univ. Press 1979 140 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 33 Analyse combinatoire Combinatieleer gtt Permutatiegroepen gtt Permutations Groupes de Combinatorial analysis Permutation groups Kombinatorik (DE-588)4031824-2 gnd rswk-swf Permutationsgruppe (DE-588)4173833-0 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s DE-604 Permutationsgruppe (DE-588)4173833-0 s White, Arthur T. Verfasser aut Früher u.d.T. Finite groups of automorphisms London Mathematical Society lecture note series 33 (DE-604)BV000000130 33 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002297952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Biggs, Norman 1941- White, Arthur T. Permutation groups and combinatorial structures London Mathematical Society lecture note series Analyse combinatoire Combinatieleer gtt Permutatiegroepen gtt Permutations Groupes de Combinatorial analysis Permutation groups Kombinatorik (DE-588)4031824-2 gnd Permutationsgruppe (DE-588)4173833-0 gnd |
| subject_GND | (DE-588)4031824-2 (DE-588)4173833-0 |
| title | Permutation groups and combinatorial structures |
| title_auth | Permutation groups and combinatorial structures |
| title_exact_search | Permutation groups and combinatorial structures |
| title_full | Permutation groups and combinatorial structures N. L. Biggs ; A. T. White |
| title_fullStr | Permutation groups and combinatorial structures N. L. Biggs ; A. T. White |
| title_full_unstemmed | Permutation groups and combinatorial structures N. L. Biggs ; A. T. White |
| title_old | Finite groups of automorphisms |
| title_short | Permutation groups and combinatorial structures |
| title_sort | permutation groups and combinatorial structures |
| topic | Analyse combinatoire Combinatieleer gtt Permutatiegroepen gtt Permutations Groupes de Combinatorial analysis Permutation groups Kombinatorik (DE-588)4031824-2 gnd Permutationsgruppe (DE-588)4173833-0 gnd |
| topic_facet | Analyse combinatoire Combinatieleer Permutatiegroepen Permutations Groupes de Combinatorial analysis Permutation groups Kombinatorik Permutationsgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002297952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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