TY  - BOOK
AU  - Sims,Charles C.
TI  - Computation with finitely presented groups
T2  - Encyclopedia of mathematics and its applications
SN  - 0521432138 (hardback)
AV  - QA171 .S6173 1993
PY  - 1994///
CY  - Cambridge [England]
PB  - Cambridge University Press
KW  - Group theory
KW  - Data processing
KW  - Finite groups
KW  - Combinatorial group theory
N1  - Includes bibliographical references (p. [581]-595) and index; 1. Basic concepts -- 2. Rewriting systems -- 3. Automata and rational languages -- 4. Subgroups of free products of cyclic groups -- 5. Coset enumeration -- 6. The Reidemeister-Schreier procedure -- 7. Generalized automata -- 8. Abelian groups -- 9. Polycyclic groups -- 10. Module bases -- 11. Quotient groups -- Appendix: Implementation issues
N2  - 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 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 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
ER  -