The bounded and precise word problems for presentations of groups /

The author introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Ivanov, Sergeĭ, 1972- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, RI : American Mathematical Society, [2020]
Colección:Memoirs of the American Mathematical Society ; no. 1281.
Temas:
Presentations of groups (Mathematics)
Word problems (Mathematics)
Présentations de groupes (Mathématiques)
Problèmes des mots (Mathématiques)
Representaciones de grupos
Lenguaje y lenguas-Frecuencia de palabras
Group theory and generalizations > Special aspects of infinite or finite groups > Generators, relations, and presentations.
Group theory and generalizations > Special aspects of infinite or finite groups > Cancellation theory; application of van Kampen diagrams [See also 57M05].
Group theory and generalizations > Special aspects of infinite or finite groups > Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08.
Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section > 04 in that area} > Theory of computing > Analysis of algorithms and problem com.
Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section > 04 in that area} > Computing methodologies and applications > Computer graphics.
Convex and discrete geometry > Polytopes and polyhedra > Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx].
Group theory and generalizations > Special aspects of infinite or finite groups > Geometric group theory [See also 05C25, 20E08, 57Mxx].
Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section > 04 in that area} > Algorithms {For numerical algorithms, see 65-XX; for combinat.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title page
  • Chapter 1. Introduction
  • Chapter 2. Preliminaries
  • Chapter 3. Proof of Proposition 1.1
  • Chapter 4. Calculus of Brackets for Group Presentation (1.2)
  • Chapter 5. Proofs of Theorem 1.2 and Corollary 1.3
  • Chapter 6. Calculus of Brackets for Group Presentation (1.4)
  • Chapter 7. Proof of Theorem 1.4
  • Chapter 8. Minimizing Diagrams over (1.2) and Proofs of Theorem 1.5 and Corollary 1.6
  • Chapter 9. Construction of Minimal Diagrams over (1.4) and Proof of Theorem 1.7
  • Chapter 10. Polygonal Curves in the Plane and Proofs of Theorems 1.8, 1.9 and Corollary 1.10

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