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Fundamental Algorithms for Permutation Groups (Lecture Notes in Computer Science), by Gregory Butler
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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.
- Sales Rank: #3780704 in Books
- Published on: 2008-06-13
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .58" w x 6.10" l, .80 pounds
- Binding: Paperback
- 244 pages
Most helpful customer reviews
3 of 3 people found the following review helpful.
Correct
By Hernadvolgyi Istvan
This book has a lot of pseudo-code. These are of the right detail and are correct. I used these algorithms (with my own modifications) to implement the Schreier-Sims method to solve Rubik's Cube - and found no mistakes or important "side issues" left out. This is a "computational" book, and not an introduction into Group Theory (or Permutation Groups), even though the concepts are briefly discussed.
1 of 1 people found the following review helpful.
A thorough view to permutation groups
By Alireza Shaneh
Written by one of the pioneers in the field, This book encompass an excellent and deep introduction to the fundamental algorithms necessary to deal with permutation groups. The algorithms are clear, concise and accurate.
2 of 4 people found the following review helpful.
Great book on the subject
By Charles Cusack
A very good book on algorithms for permutation groups. The author gives many references for each chapter, which are useful for further study.
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