+612 9045 4394
Fundamental Algorithms for Permutation Groups : Lecture Notes in Computer Science - Gregory Butler

Fundamental Algorithms for Permutation Groups

Lecture Notes in Computer Science

Paperback Published: 27th November 1991
ISBN: 9783540549550
Number Of Pages: 244

Share This Book:


or 4 easy payments of $27.76 with Learn more
Ships in 7 to 10 business days

This is the first-ever book on computational group theory.It provides extensive and up-to-date coverage of thefundamental algorithms for permutation groups with referenceto aspects of combinatorial group theory, soluble groups,and p-groups where appropriate.The book begins with a constructive introduction to grouptheory and algorithms for computing with small groups,followed by a gradual discussion of the basic ideas of Simsfor computing with very large permutation groups, andconcludes with algorithms that use group homomorphisms, asin the computation of Sylowsubgroups. No background ingroup theory is assumed.The emphasis is on the details of the data structures andimplementation which makes the algorithms effective whenapplied to realistic problems. The algorithms are developedhand-in-hand with the theoretical and practicaljustification.All algorithms are clearly described,examples are given, exercises reinforce understanding, anddetailed bibliographical remarks explain the history andcontext of the work.Much of the later material on homomorphisms, Sylowsubgroups, and soluble permutation groups is new.

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.

ISBN: 9783540549550
ISBN-10: 3540549552
Series: Lecture Notes in Computer Science
Audience: General
Format: Paperback
Language: English
Number Of Pages: 244
Published: 27th November 1991
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.37
Weight (kg): 0.36