Computation with finitely presented groups
By: Charles C. Sims
Series: Encyclopedia of mathematics and its applications -- no. 48
Publisher: Cambridge University Press
Published: 2010
Place of publication: Cambridge
Language: eng
ISBN-13: 9780521135078
Subjects: Group theory; Finite groups; Combinatorial group theory; Data processing
Description: Research in computational group theory, an active subfield of computational algebra, has emphasized four areas: finite permutation groups, finite solvable groups, matrix representations of finite groups, and finitely presented groups. This book deals with the last of these areas. It is the first text to present the fundamental algorithmic ideas which have been developed to compute with finitely presented groups that are infinite, or at least not obviously finite.

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.
Notes: Originally published: 1994.

Includes bibliographical references and index.
Table of contents: title: 1. Basic concepts; title: 2. Rewriting systems; title: 3. Automata and rational languages; title: 4. Subgroups of free products of cyclic groups; title: 5. Coset enumeration; title: 6. The Reidemeister-Schreier procedure; title: 7. Generalized automata; title: 8. Abelian groups; title: 9. Polycyclic groups; title: 10. Module bases; title: 11. Quotient groups; title: Appendix: Implementation issues.