Fundamental algorithms for permutation groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1991
|
| Series: | Lecture notes in computer science
559 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 238 S. |
| ISBN: | 3540549552 0387549552 |
Staff View
MARC
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| 245 | 1 | 0 | |a Fundamental algorithms for permutation groups |c G. Butler |
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| 300 | |a XII, 238 S. | ||
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Record in the Search Index
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Contents
Part 1: Small Groups
1. Introduction 1
Machine Representation of Groups — Systems — Some Applications
Bibliographical Remarks
2. Group Theory Background 7
Groups — Permutations — Subgroups and Cosets — Conjugates and Normal
Subgroups — Commuting Elements — Exercises
Bibliographical Remarks
3. List of Elements 14
Obvious Approach from First Principles — A Trivial Improvement — Induc¬
tion on the Length of Products — One Generator Groups — Induction on the
Generators — Simple Algorithm of Dimino — Complete Algorithm of Dimino
— Uses — Summary — Exercises
Bibliographical Remarks
4. Searching Small Groups 24
Linear Search of the List of Elements — Searching as a Discarding Process —
Another Example — Finding All Elements — Analysis — Multiple Discarding
— Summary — Exercises
Bibliographical Remarks
5. Cayley Graph and Defining Relations 33
Definitions — Start with a Spanning Tree — The Colouring Algorithm —
Example — Another Example — Analysis — Summary — Exercises
Bibliographical Remarks
6. Lattice of Subgroups 44
Lattices and Layers — Constructing the Next Layer — How to Test a Sub¬
group is New — Eliminating the Normality Test — Using Elements of Prime
Power Order — Using Subgroups of Prime Power Order — Full Lattice Algo¬
rithm for Soluble Subgroups — Analysis — Saving Space — Perfect Subgroups
— Summary — Exercises
Bibliographical Remarks
Part 2: Permutation Groups
7. Orbits and Schreier Vectors 56
Orbits — Schreier Vectors — Analysis of Algorithm 3 — Summary — Exer¬
cises
Bibliographical Remarks
8. Regularity 64
Definitions and a First Algorithm — Parallel Testing of Regularity — Testing
Semiregularity — Summary — Exercises
Bibliographical Remarks
9. Primitivity 71
Definitions — Finest Invariant Partition — Eliminating Redundant Checking
— Testing Primitivity — Summary — Exercises
Bibliographical Remarks
10. Inductive Foundation 78
Definitions — Examples — Representing Elements and Testing Membership
— Enumerating All Elements — Summary — Exercises
Bibliographical Remarks
11. Backtrack Search 98
Strong Generators of the Subgroup — First in Orbit — Restrictions on Im¬
age Points — Choosing an Appropriate Base — Using a Known Subgroup —
Searching Images of an Initial Base Segment — More on Cosets — Preprocess¬
ing — Case Study 1: Centralizer — Case Study 2: Normalizer— Case Study
3: Intersection — Case Study 4: Set Stabiliser — Summary — Exercises
Bibliographical Remarks
12. Base Change 117
Other Bases — Interchanging Adjacent Base Points — Example — Exam¬
ple — Analysis of Interchanging Base Points — Removing Redundant Strong
Generators — Conjugation and the Complete Algorithm — Example — Sum¬
mary — Exercises
Bibliographical Remarks
13. Schreier Sims Method 129
Verifying Strong Generation — Schreier Generators — Example — Avoid
Rechecking Schreier Generators — Stripping Schreier Generators — Variations
of the Schreier Sims Method — Summary — Exercises
Bibliographical Remarks
14. Complexity of the Schreier Sims Method 143
Furst, Hopcroft, and Luks — Knuth — Jerrum — Summary — Exercises
Bibliographical Remarks
Part 3: Homomorphisms and Their Use
15. Homomorphisms 156
Homomorphisms — Overview — Transitive Constituent Homomorphism —
Blocks Homomorphism — Other Homomorphisms — Summary — Exercises
Bibliographical Remarks
16. Sylow Subgroups 171
Homomorphic Images of Centralizers — Restricting to Orbits — Finding Cen
tralizers — Random Elements — More on Blocks Homomorphisms — Primi¬
tive Groups — Summary — Exercises
Bibliographical Remarks
17. P Groups and Soluble Groups 184
Presentations — PC Presentations of Soluble Groups — PC Presentations
of p Groups — Collection — Consistency — Elements and Subgroups of p
Groups — Conjugacy Classes of Elements of p Groups — Sylow Subgroups of
Soluble Groups — Summary — Exercises
Bibliographical Remarks
18. Soluble Permutation Groups 205
Combining Series Generators and Strong Generators — Cyclically Extended
Schreier Vectors — Using Homomorphisms — Computing with the Isomor¬
phism — Subnormal Series: p Groups — Subnormal Series: Soluble Groups
— Subnormal Series: Soluble Schreier Method — Conditioned PC Presen¬
tation of a p Group — Conditioned PC Presentation of a Soluble Group —
Summary — Exercises
Bibliographical Remarks
19. Some Other Algorithms 229
Single Coset Enumeration — Double Coset Enumeration — Verify — Conju¬
gacy Classes of Elements — Cohomology — Group Recognition — Composi¬
tion factors — Some Ideas From Complexity Results
Index of Algorithms 233
Index of Definitions 236 |
| any_adam_object | 1 |
| author | Butler, Gregory 1953- |
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| ctrlnum | (OCoLC)231254092 (DE-599)BVBBV004629793 |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV004629793 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T15:06:07Z |
| institution | BVB |
| isbn | 3540549552 0387549552 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002842960 |
| oclc_num | 231254092 |
| open_access_boolean | |
| owner | DE-384 DE-19 DE-BY-UBM DE-12 DE-703 DE-739 DE-20 DE-91G DE-BY-TUM DE-706 DE-83 DE-188 DE-11 |
| owner_facet | DE-384 DE-19 DE-BY-UBM DE-12 DE-703 DE-739 DE-20 DE-91G DE-BY-TUM DE-706 DE-83 DE-188 DE-11 |
| physical | XII, 238 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in computer science |
| series2 | Lecture notes in computer science |
| spelling | Butler, Gregory 1953- Verfasser (DE-588)1022348884 aut Fundamental algorithms for permutation groups G. Butler Berlin [u.a.] Springer 1991 XII, 238 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in computer science 559 Algorithms Permutation groups Permutationsgruppe (DE-588)4173833-0 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Permutationsgruppe (DE-588)4173833-0 s Algorithmus (DE-588)4001183-5 s DE-604 Gruppentheorie (DE-588)4072157-7 s Lecture notes in computer science 559 (DE-604)BV000000607 559 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002842960&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Butler, Gregory 1953- Fundamental algorithms for permutation groups Lecture notes in computer science Algorithms Permutation groups Permutationsgruppe (DE-588)4173833-0 gnd Gruppentheorie (DE-588)4072157-7 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4173833-0 (DE-588)4072157-7 (DE-588)4001183-5 |
| title | Fundamental algorithms for permutation groups |
| title_auth | Fundamental algorithms for permutation groups |
| title_exact_search | Fundamental algorithms for permutation groups |
| title_full | Fundamental algorithms for permutation groups G. Butler |
| title_fullStr | Fundamental algorithms for permutation groups G. Butler |
| title_full_unstemmed | Fundamental algorithms for permutation groups G. Butler |
| title_short | Fundamental algorithms for permutation groups |
| title_sort | fundamental algorithms for permutation groups |
| topic | Algorithms Permutation groups Permutationsgruppe (DE-588)4173833-0 gnd Gruppentheorie (DE-588)4072157-7 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Algorithms Permutation groups Permutationsgruppe Gruppentheorie Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002842960&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000607 |
| work_keys_str_mv | AT butlergregory fundamentalalgorithmsforpermutationgroups |