000			02958cam a2200361 a 4500
001			0000025588
005			20230921135913.0
008			920903s1994 enkm b a001 0 eng
010			_a92032383
020			_a0521432138 (hardback)
020			_a9780521432139 (hardback)
035			_a(OCoLC)26672381
050	0	0	_aQA171 _b.S6173 1993
100	1		_aSims, Charles C.
245	1	0	_aComputation with finitely presented groups / _cby Charles C. Sims.
260			_aCambridge [England] : _bCambridge University Press, _c1994.
264			_aCambridge [England] : _bCambridge University Press, _c1994
300			_axiii, 604 pages : _billustrations ; _c25 cm.
490	1		_aEncyclopedia of mathematics and its applications ; _vv. 48.
504			_aIncludes bibliographical references (p. [581]-595) and index.
505	0		_a1. 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.
520			_aResearch 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.
520	8		_aThe 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.
520	8		_aThe 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.
650		0	_aGroup theory _xData processing.
650		0	_aFinite groups _xData processing.
650		0	_aCombinatorial group theory _xData processing.
830		0	_aEncyclopedia of mathematics and its applications ; _vv. 48.
908			_a150422
913			_aN
989			_a20230822095114.0
999			_c13430 _d13430