Automatic Groups Associated with Word Orders Other than Shortlex

DOI10.1142/S0218196798000272zbMath0942.20012arXivmath/9705208MaRDI QIDQ4704557

Sarah Rees

Publication date: 13 August 2000

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9705208

zbMATH Keywords

algorithmsBaumslag-Solitar groupsautomatic groupsword orderswreath product orders

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Generators, relations, and presentations of groups (20F05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Software, source code, etc. for problems pertaining to group theory (20-04) Word problems, etc. in computability and recursion theory (03D40)

Cites Work

• Small cancellation theory and automatic groups
• Artin groups of finite type are biautomatic
• The combinatorial structure of cocompact discrete hyperbolic groups
• The use of Knuth-Bendix methods to solve the word problem in automatic groups
• Presentations of groups and monoids
• A finiteness property and an automatic structure for Coxeter groups
• Rewriting systems of Coxeter groups
• Geodesic automation and growth functions for Artin groups of finite type
• Strongly geodesically automatic groups are hyperbolic
• Artin groups of extra-large type are biautomatic
• A quadratic parabolic group
• Discrete parabolic representations of link groups
• A REMARK ABOUT COMBINGS OF GROUPS
• Mapping class groups are automatic