Permutation group algorithms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
2003
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
152 |
| Schlagworte: | |
| Online-Zugang: | Sample text Table of contents Publisher description Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 254-261) and index |
| Beschreibung: | ix, 264 p. 23 cm |
| ISBN: | 052166103X |
Internformat
MARC
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| 490 | 1 | |a Cambridge tracts in mathematics |v 152 | |
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| 650 | 4 | |a Permutation groups | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
1 Introduction page 1
1.1 A List of Algorithms 4
1.2 Notation and Terminology 6
1.2.1 Groups 7
1.2.2 Permutation Groups 9
1.2.3 Algorithmic Concepts 10
1.2.4 Graphs 11
1.3 Classification of Randomized Algorithms 12
2 Black Box Groups 16
2.1 Closure Algorithms 18
2.1.1 Orbit Computations 18
2.1.2 Closure of Algebraic Structures 23
2.2 Random Elements of Black Box Groups 24
2.3 Random Subproducts 30
2.3.1 Definition and Basic Properties 30
2.3.2 Reducing the Number of Generators 33
2.3.3 Closure Algorithms without Membership Testing 37
2.3.4 Derived and Lower Central Series 38
2.4 Random Prefixes 40
2.4.1 Definition and Basic Properties 40
2.4.2 Applications 44
3 Permutation Groups: A Complexity Overview 48
3.1 Polynomial Time Algorithms 48
3.2 Nearly Linear Time Algorithms 51
3.3 Non Polynomial Time Methods 52
vii
viii Contents
4 Bases and Strong Generating Sets 55
4.1 Basic Definitions 55
4.2 The Schreier Sims Algorithm 57
4.3 The Power of Randomization 62
4.4 Shallow Schreier Trees 64
4.5 Strong Generators in Nearly Linear Time 70
4.5.1 Implementation 75
5 Further Low Level Algorithms 79
5.1 Consequences of the Schreier Sims Method 79
5.1.1 Pointwise Stabilizers 79
5.1.2 Homomorphisms 80
5.1.3 Transitive Constituent and Block
Homomorphisms 81
5.1.4 Closures and Normal Closures 83
5.2 Working with Base Images 84
5.3 Permutation Groups as Black Box Groups 93
5.4 Base Change 97
5.5 Blocks of Imprimitivity 100
5.5.1 Blocks in Nearly Linear Time 101
5.5.2 The Smallest Block Containing a Given Subset 107
5.5.3 Structure Forests 111
6 A Library of Nearly Linear Time Algorithms 114
6.1 A Special Case of Group Intersection and Applications 115
6.1.1 Intersection with a Normal Closure 115
6.1.2 Centralizer in the Symmetric Group 117
6.1.3 The Center 120
6.1.4 Centralizer of a Normal Subgroup 120
6.1.5 Core of a Subnormal Subgroup 124
6.2 Composition Series 125
6.2.1 Reduction to the Primitive Case 126
6.2.2 The O Nan Scott Theorem 129
6.2.3 Normal Subgroups with Nontrivial Centralizer 133
6.2.4 Groups with a Unique Nonabelian Minimal
Normal Subgroup 139
6.2.5 Implementation 146
6.2.6 An Elementary Version 149
6.2.7 Chief Series 155
6.3 Quotients with Small Permutation Degree 156
6.3.1 Solvable Radical and p Core 157
Contents ix
7 Solvable Permutation Groups 162
7.1 Strong Generators in Solvable Groups 162
7.2 Power Conjugate Presentations 165
7.3 Working with Elementary Abelian Layers 166
7.3.1 Sylow Subgroups 167
7.3.2 Conjugacy Classes in Solvable Groups 172
7.4 Two Algorithms for Nilpotent Groups 175
7.4.1 A Fast Nilpotency Test 176
7.4.2 The Upper Central Series in Nilpotent Groups 179
8 Strong Generating Tests 183
8.1 The Schreier Todd Coxeter Sims Procedure 184
8.1.1 Coset Enumeration 184
8.1.2 Leon s Algorithm 186
8.2 Sims s Verify Routine 188
8.3 Toward Strong Generators by a Las Vegas Algorithm 191
8.4 A Short Presentation 197
9 Backtrack Methods 201
9.1 Traditional Backtrack 202
9.1.1 Pruning the Search Tree: Problem Independent
Methods 203
9.1.2 Pruning the Search Tree: Problem Dependent
Methods 205
9.2 The Partition Method 207
9.3 Normalizers 211
9.4 Conjugacy Classes 214
10 Large Base Groups 218
10.1 Labeled Branchings 218
10.1.1 Construction 222
10.2 Alternating and Symmetric Groups 225
10.2.1 Number Theoretic and Probabilistic Estimates 228
10.2.2 Constructive Recognition: Finding the
New Generators 235
10.2.3 Constructive Recognition: The Homomorphism k 239
10.2.4 Constructive Recognition: The Case of Giants 244
10.3 A Randomized Strong Generator Construction 246
Bibliography 254
Index 262
|
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| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV014403482 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:02:25Z |
| institution | BVB |
| isbn | 052166103X |
| language | English |
| lccn | 2002022291 |
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| oclc_num | 49225699 |
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| physical | ix, 264 p. 23 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge University Press |
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| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Seress, Ákos Verfasser aut Permutation group algorithms Ákos Seress 1. publ. Cambridge [u.a.] Cambridge University Press 2003 ix, 264 p. 23 cm txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 152 Includes bibliographical references (p. 254-261) and index Algorithms Permutation groups Permutationsgruppe (DE-588)4173833-0 gnd rswk-swf Algorithmische Gruppentheorie (DE-588)4705829-8 gnd rswk-swf Permutationsgruppe (DE-588)4173833-0 s Algorithmische Gruppentheorie (DE-588)4705829-8 s DE-604 Cambridge tracts in mathematics 152 (DE-604)BV000000001 152 http://www.loc.gov/catdir/samples/cam033/2002022291.html Sample text http://www.loc.gov/catdir/toc/cam023/2002022291.html Table of contents http://www.loc.gov/catdir/description/cam022/2002022291.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009855506&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Seress, Ákos Permutation group algorithms Cambridge tracts in mathematics Algorithms Permutation groups Permutationsgruppe (DE-588)4173833-0 gnd Algorithmische Gruppentheorie (DE-588)4705829-8 gnd |
| subject_GND | (DE-588)4173833-0 (DE-588)4705829-8 |
| title | Permutation group algorithms |
| title_auth | Permutation group algorithms |
| title_exact_search | Permutation group algorithms |
| title_full | Permutation group algorithms Ákos Seress |
| title_fullStr | Permutation group algorithms Ákos Seress |
| title_full_unstemmed | Permutation group algorithms Ákos Seress |
| title_short | Permutation group algorithms |
| title_sort | permutation group algorithms |
| topic | Algorithms Permutation groups Permutationsgruppe (DE-588)4173833-0 gnd Algorithmische Gruppentheorie (DE-588)4705829-8 gnd |
| topic_facet | Algorithms Permutation groups Permutationsgruppe Algorithmische Gruppentheorie |
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