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

Sims, Charles C.

ISBN 10: 0521432138 / ISBN 13: 9780521432139

Edité par Cambridge University Press, 1994

A propos de cet article

N° de réf. du vendeur I-9780521432139

Détails bibliographiques

• Titre: Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications, Series Number 48)
• Éditeur: Cambridge University Press
• Date de parution: 1994
• Langue: anglais
• ISBN à 10 chiffres: 0521432138
• ISBN à 13 chiffres: 9780521432139
• Reliure: Couverture rigide
• État de l'article: New

A propos de ce titre

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.