Computation with Finitely Presented Groups (Encyclopedia of Mathematics and Its Applications): 48 (Encyclopedia of Mathematics and its Applications, Series Number 48) - Hardcover

Sims, Charles C.

Hardcover

ISBN 10: 0521432138 ISBN 13: 9780521432139

Publisher: Cambridge University Press, 1994

Synopsis

Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises 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 generalisation of Buchberger's Gröbner 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.

About this title

Review

"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

Book Description

It is a comprehensive text presenting 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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1994
• Language: English
• ISBN 10: 0521432138
• ISBN 13: 9780521432139
• Binding: Hardcover
• Number of pages: 624