Fundamental algorithms for permutation groups
Author(s)
Bibliographic Information
Fundamental algorithms for permutation groups
（Lecture notes in computer science, 559）
Springer-Verlag, c1991
- : gw
- : us
Available at / 53 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Kochi University of Technology.Library
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University of Tsukuba Library, Library on Library and Information Science
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Note
Includes bibliographical references and indexes
Description and Table of Contents
Description
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.
Table of Contents
Group theory background.- List of elements.- Searching small groups.- Cayley graph and defining relations.- Lattice of subgroups.- Orbits and schreier vectors.- Regularity.- Primitivity.- Inductive foundation.- Backtrack search.- Base change.- Schreier-Sims method.- Complexity of the Schreier-Sims method.- Homomorphisms.- Sylow subgroups.- P-groups and soluble groups.- Soluble permutation groups.- Some other algorithms.
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