Permutation Group Algorithms. (Record no. 76491)

MARC details
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fixed length control field 06873nam a22004813i 4500
001 - CONTROL NUMBER
control field EBC217726
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20191126103235.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
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007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
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008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 191125s2003 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781139146166
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9780521661034
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC217726
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL217726
035 ## - SYSTEM CONTROL NUMBER
System control number (CaPaEBR)ebr10069986
035 ## - SYSTEM CONTROL NUMBER
System control number (CaONFJC)MIL41763
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)668199608
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA175 .S47 2003
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.2
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Seress, Ákos.
9 (RLIN) 52998
245 10 - TITLE STATEMENT
Title Permutation Group Algorithms.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture New York :
Name of producer, publisher, distributor, manufacturer Cambridge University Press,
Date of production, publication, distribution, manufacture, or copyright notice 2003.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2003.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (274 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
490 1# - SERIES STATEMENT
Series statement Cambridge Tracts in Mathematics ;
Volume/sequential designation v.152
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Cover -- Half-title -- Title -- Copyright -- Contents -- 1 Introduction -- Acknowledgments -- 1.1. List of Algorithms -- 1.2. Notation and Terminology -- 1.2.1. Groups -- 1.2.2. Permutation Groups -- 1.2.3. Algorithmic Concepts -- 1.2.4. Graphs -- 1.3.Classification of Randomized Algorithms -- 2 Black-Box Groups -- 2.1. Closure Algorithms -- 2.1.1. Orbit Computations -- 2.1.2.Closure of Algebraic Structures -- The Closure Algorithm -- Algorithms Based on Normal Closure -- 2.2. Random Elements of Black-Box Groups -- The Product Replacement Algorithm -- 2.3. Random Subproducts -- 2.3.1. Definition and Basic Properties -- 2.3.2. Reducing the Number of Generators -- 2.3.3. Closure Algorithms without Membership Testing -- 2.3.4. Derived and Lower Central Series -- 2.4. Random Prefixes -- 2.4.1. Definition and Basic Properties -- 2.4.2. Applications -- Exercises -- 3 Permutation Groups A Complexity Overview -- 3.1. Polynomial-Time Algorithms -- 3.2. Nearly Linear-Time Algorithms -- 3.3. Non-Polynomial-Time Methods -- 4 Bases and Strong Generating Sets -- 4.1. Basic Definitions -- The Sifting Procedure -- 4.2. The Schreier-Sims Algorithm -- The Schreier-Sims Algorithm -- 4.3. The Power of Randomization -- The Random Schreier-Sims Algorithm -- 4.4. Shallow Schreier Trees -- 4.5. Strong Generators in Nearly Linear Time -- The SGS Construction -- The Algorithm Solving (4.6) -- 4.5.1. Implementation -- Exercises -- 5 Further Low-Level Algorithms -- 5.1. Consequences of the Schreier-Sims Method -- 5.1.1. Pointwise Stabilizers -- 5.1.2. Homomorphisms -- 5.1.3. Transitive Constituent and Block Homomorphisms -- The Block Homomorphism Algorithm -- 5.1.4. Closures and Normal Closures -- 5.2. Working with Base Images -- 5.3. Permutation Groups as Black-Box Groups -- Representation as a Black-Box Group -- 5.4. Base Change.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note The Exchange of Two Base Points (Deterministic Version) -- The Exchange of Two Base Points (Las Vegas Version) -- Base Change by Conjugation -- 5.5. Blocks of Imprimitivity -- 5.5.1. Blocks in Nearly Linear Time -- 5.5.2. The Smallest Block Containing a Given Subset -- Computation of the Smallest Block Containing… -- 5.5.3. Structure Forests -- Exercises -- 6 A Library of Nearly Linear-Time Algorithms -- 6.1. Special Case of Group Intersection and pplications -- 6.1.1. Intersection with a Normal Closure -- 6.1.2. Centralizer in the Symmetric Group -- 6.1.3. The Center -- 6.1.4. Centralizer of a Normal Subgroup -- 6.1.5. Core of a Subnormal Subgroup -- 6.2. Composition Series -- 6.2.1. Reduction to the Primitive Case -- 6.2.2. The O'Nan-Scott Theorem -- 6.2.3. Normal Subgroups with Nontrivial Centralizer -- Computing the Socle of a Frobenius Group -- Luks's Algorithm -- Neumann's Algorithm (the EARNS Subroutine) -- 6.2.4. Groups with a Unique Nonabelian Minimal Normal Subgroup -- The Algorithm for Case B of Theorem 6.2.7 -- The Algorithm for Case C(i) -- The Algorithm for Case C(ii) -- The Algorithm for Case C(iii) -- 6.2.5. Implementation -- 6.2.6. An Elementary Version -- Beals's Algorithm for Groups with Regular Normal Subgroups -- Beals's Algorithm for Groups with No Regular Normal Subgroups -- 6.2.7. Chief Series -- 6.3. Quotients with Small Permutation Degree -- 6.3.1. Solvable Radical and p-Core -- The Algorithms -- Exercises -- 7 Solvable Permutation Groups -- 7.1. Strong Generators in Solvable Groups -- The Generalized Normal Closure Algorithm -- 7.2. Power-Conjugate Presentations -- Conversion to a pcp -- 7.3. Working with Elementary Abelian Layers -- 7.3.1. Sylow Subgroups -- 7.3.2. Conjugacy Classes in Solvable Groups -- Computation of the Class Representatives -- Computation of the Centralizers -- 7.4. Two Algorithms for Nilpotent Groups.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 7.4.1. A Fast Nilpotency Test -- 7.4.2. The Upper Central Series in Nilpotent Groups -- Exercises -- 8 Strong Generating Tests -- 8.1. The Schreier-Todd-Coxeter-Sims Procedure -- 8.1.1. Coset Enumeration -- 8.1.2. Leon's Algorithm -- The STCS Algorithm -- 8.2. Sims's Verify Routine -- The Verify Routine -- 8.3. Toward Strong Generators by a Las Vegas Algorithm -- 8.4. Short Presentation -- 9 Backtrack Methods -- 9.1. Traditional Backtrack -- 9.1.1. Pruning the Search Tree: Problem-Independent Methods -- 9.1.2. Pruning the Search Tree: Problem-Dependent Methods -- 9.2. The Partition Method -- 9.3. Normalizers -- 9.4. Conjugacy Classes -- Class Representatives by Random Sampling -- Representatives in Centralizers of p-Elements -- Separation of the Solvable Radical -- Exercises -- 10 Large-Base Groups -- 10.1. Labeled Branchings -- 10.1.1. Construction -- 10.2. Alternating and Symmetric Groups -- 10.2.1. Number Theoretic and Probabilistic Estimates -- 10.2.2. Constructive Recognition: Finding the New Generators -- 10.2.3. Constructive Recognition: The Homomorphism Lambda -- Summary of the Proof of Theorem 10.2.4(a) -- Proof of Theorem 10.2.4(b) -- 10.2.4. Constructive Recognition: The Case of Giants -- 10.3. A Randomized Strong Generator Construction -- Bibliography -- Index.
520 ## - SUMMARY, ETC.
Summary, etc. Theory of permutation group algorithms for graduates and above. Exercises and hints for implementation throughout.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Permutation groups.
9 (RLIN) 52999
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
9 (RLIN) 53000
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Seress, Ákos
Title Permutation Group Algorithms
Place, publisher, and date of publication New York : Cambridge University Press,c2003
International Standard Book Number 9780521661034
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Cambridge Tracts in Mathematics
9 (RLIN) 53001
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/thebc/detail.action?docID=217726">https://ebookcentral.proquest.com/lib/thebc/detail.action?docID=217726</a>
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Content of non-MARC field EBK
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