Computation with finitely presented groups

Charles C. Sims

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 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.

「Nielsen BookData」より

[目次]

  • 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.

「Nielsen BookData」より

この本の情報

書名 Computation with finitely presented groups
著作者等 Sims, Charles C
Doran B.
Flajolet Philippe
Ismail M.
Lam T. Y.
Lutwak E.
Rota G.-C.
Wutwak E.
Sims Charles C.
シリーズ名 Encyclopedia of mathematics and its applications
出版元 Cambridge University Press
刊行年月 1994
ページ数 xiii, 604 p.
大きさ 25 cm
ISBN 0521432138
NCID BA21748237
※クリックでCiNii Booksを表示
言語 英語
出版国 イギリス
この本を: 
このエントリーをはてなブックマークに追加

このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想