Computation with Finitely Presented Groups (Hardcover)

Descripción

Hardcover. 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. The book describes methods for working with elements, subgroups, and quotient groups of a finitely presented group. The author emphasizes the connection with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, from computational number theory, and from computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms are used to study the Abelian quotients of a finitely presented group. The work of Baumslag, Cannonito, and Miller on computing non-Abelian 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

N° de ref. del artículo 9780521432139

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Detalles bibliográficos

Título

Computation with Finitely Presented Groups (Hardcover)

Editor

Cambridge University Press, Cambridge

Fecha de publicación

1994

Idioma

Inglés

ISBN 10

0521432138

ISBN 13

9780521432139

Encuadernación

Hardcover

Estado

new

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