Fundamental Algorithms for Permutation Groups

Gregory Butler

ISBN 10: 3540549552 / ISBN 13: 9783540549550

Published by Springer Berlin Heidelberg, Springer Berlin Heidelberg Nov 1991, 1991

About this Item

Neuware -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 groupsand p-groups where appropriate.The book begins with a constructive introduction to grouptheory and algorithms for computing with small groupsfollowed 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 describedexamples 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 256 pp. Englisch.

Seller Inventory # 9783540549550

Bibliographic Details

• Title: Fundamental Algorithms for Permutation Groups
• Publisher: Springer Berlin Heidelberg, Springer Berlin Heidelberg Nov 1991
• Publication Date: 1991
• Language: English
• ISBN 10: 3540549552
• ISBN 13: 9783540549550
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

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.