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Computation with Finitely Presented Groups : Encyclopedia of Mathematics and Its Applications - Charles C. Sims

Computation with Finitely Presented Groups

Encyclopedia of Mathematics and Its Applications

Hardcover Published: 28th January 1994
ISBN: 9780521432139
Number Of Pages: 624

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Research in computational group theory, an active subfield of computational algebra, has emphasized three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. It is the first text to present the fundamental algorithmic ideas which have been developed to compute with finitely presented groups, discussing techniques for computing with finitely presented groups which are infinite, or at least not obviously finite, and describing methods for working with elements, subgroups, and quotient groups of a finitely presented group. The author emphasizes the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito, and Miller on computing nonabelian polycyclic quotients is described as a generalization of Buchberger's Grobner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups, and theoretical computer scientists will find this book useful.

"this book is a very interesting treatment of the computational aspects of combinatorial group theory. It is well-written, nicely illustrating the algorithms presented with many examples. Also, some remarks on the history of the field are included. In adition, many exercises are provided throughout...this is a very valuable book that is well-suited as a textbook for a graduate course on computational group theory. It addresses students of mahtematics and of computer science alike, providing the necessary background for both. In addition, this book will be of good use as a reference source for computational aspects of combinatorial group theory." Friedrich Otto, Mathematical Reviews

Basic concepts
Rewriting systems
Automata and rational languages
Subgroups of free products of cyclic groups
Coset enumeration
The Reidemeister-Schreier procedure
Generalized automata
Abelian groups
Polycyclic groups
Module bases
Quotient groups
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521432139
ISBN-10: 0521432138
Series: Encyclopedia of Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 624
Published: 28th January 1994
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.4 x 15.6  x 3.3
Weight (kg): 1.04