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Description - Computation with Finitely Presented Groups by Charles C. Sims

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.

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Book Details

ISBN: 9780521432139
ISBN-10: 0521432138
Format: Hardback
(234mm x 156mm x 33mm)
Pages: 624
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 28-Jan-1994
Country of Publication: United Kingdom

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Books By Charles C. Sims

Computation with Finitely Presented Groups by Charles C. Sims
Paperback, February 2010
$139.50