zbMATH — the first resource for mathematics

On Artin groups and Coxeter groups of large type. (English) Zbl 0576.20021
Contributions to group theory, Contemp. Math. 33, 50-78 (1984).
[For the entire collection see Zbl 0539.00007.]
Let \(M=(m_{ij};\;i,j\in I)\) be a Coxeter matrix. The Artin group \(G(M)\) of large type \((m_{ij}\geq~3; i\neq j)\) is torsion-free, the set \(\{a^ 2_ i,\;i\in I\}\) freely generates a free subgroup of \(G(M)\), the conjugacy problem in \(G(M)\) (as in the Coxeter groups of large type) is solvable.

20F36 Braid groups; Artin groups
20F05 Generators, relations, and presentations of groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20F55 Reflection and Coxeter groups (group-theoretic aspects)