TY  - BOOK
AU  - Sims,Charles C.
TI  - Computation with finitely presented groups
T2  - Encyclopedia of mathematics and its applications 
SN  - 9780521135078 (pbk.)
AV  - QA171 
U1  - 512.2 22
PY  - 2010///
CY  - Cambridge 
PB  - Cambridge University Press
KW  - Group theory
KW  - Data processing
KW  - Finite groups
KW  - Combinatorial group theory
N1  - 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; Includes bibliographical references 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
ER  -