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About this book
This is the first-ever book on computational group theory.
It provides extensive and up-to-date coverage of the
fundamental algorithms for permutation groups with reference
to aspects of combinatorial group theory, soluble groups,
and p-groups where appropriate.
The book begins with a constructive introduction to group
theory and algorithms for computing with small groups,
followed by a gradual discussion of the basic ideas of Sims
for computing with very large permutation groups, and
concludes with algorithms that use group homomorphisms, as
in the computation of Sylowsubgroups. No background in
group theory is assumed.
The emphasis is on the details of the data structures and
implementation which makes the algorithms effective when
applied to realistic problems. The algorithms are developed
hand-in-hand with the theoretical and practical
justification.All algorithms are clearly described,
examples are given, exercises reinforce understanding, and
detailed bibliographical remarks explain the history and
context of the work.
Much of the later material on homomorphisms, Sylow
subgroups, and soluble permutation groups is new.
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Keywords
- Algebraic Algorithms
- Algebraische Algorithmen
- Computational Complexity
- Computational Group Theory
- Graph
- Graph Algorithms
- Graph-Algorithmen
- Group theory
- Komplexität und Algorithmen
- Permutatioen und Kombinationen
- Permutations and Combinations
- algorithms
- data structures
- algorithm analysis and problem complexity
- combinatorics
Table of contents (19 chapters)
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Front Matter
Bibliographic Information
Book Title: Fundamental Algorithms for Permutation Groups
Editors: G. Butler
Series Title: Lecture Notes in Computer Science
DOI: https://doi.org/10.1007/3-540-54955-2
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1991
Softcover ISBN: 978-3-540-54955-0Published: 27 November 1991
eBook ISBN: 978-3-540-46607-9Published: 03 July 2005
Series ISSN: 0302-9743
Series E-ISSN: 1611-3349
Edition Number: 1
Number of Pages: XII, 244
Topics: Theory of Computation, Group Theory and Generalizations, Discrete Mathematics, Symbolic and Algebraic Manipulation, Algorithm Analysis and Problem Complexity, Combinatorics