Computation with Finitely Presented Groups
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Computation with Finitely Presented Groups by Charles C. Sims
Book DescriptionResearch 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 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 DetailsISBN: 9780521432139
(234mm x 156mm x 33mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 28-Jan-1994
Country of Publication: United Kingdom
Books By Author Charles C. Sims
Computation with Finitely Presented Groups, Paperback (March 2010)» View all books by Charles C. Sims
This book describes the basic algorithmic ideas behind accepted methods for computing with finitely presented groups.
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