Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications)

Sims, Charles C.

ISBN 10: 0521135079 / ISBN 13: 9780521135078

Edité par Cambridge University Press, 2010

N° de réf. du vendeur 161455

Synopsis :

This book describes the basic algorithmic ideas behind accepted methods for computing with finitely presented groups.

Présentation de l'éditeur: 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.

Détails bibliographiques

Titre : Computation with Finitely Presented Groups (...
Éditeur : Cambridge University Press
Date d'édition : 2010
Reliure : Couverture souple
Etat : New