Umfang:
1 Online-Ressource (xiii, 604 pages)
,
digital, PDF file(s).
ISBN:
9780511574702
Serie:
Encyclopedia of mathematics and its applications volume 48
Inhalt:
Research 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 Gröbner 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.
Inhalt:
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
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Weitere Ausg.:
ISBN 9780521135078
Weitere Ausg.:
ISBN 9780521432139
Weitere Ausg.:
ISBN 9780521432139
Weitere Ausg.:
ISBN 9780521135078
Weitere Ausg.:
Erscheint auch als Sims, Charles C. Computation with finitely presented groups Cambridge [u.a.] : Cambridge Univ. Press, 1994 ISBN 0521432138
Weitere Ausg.:
Print version ISBN 9780521432139
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Gruppentheorie
;
Datenverarbeitung
;
Endliche Gruppe
;
Datenverarbeitung
;
Kombinatorische Gruppentheorie
;
Datenverarbeitung
DOI:
10.1017/CBO9780511574702
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