Fundamental Algorithms for Permutation Groups

1991
ISBN: 978-3-540-54955-0
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 559, 244 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 394 g

Reihe: Lecture Notes in Computer Science

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.

Zielgruppe

Research

Autoren/Hrsg.

Butler, Gregory

Fachgebiete

• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.