منابع مشابه
Artin Groups and Coxeter Groups
where the words on each side of these relations are sequences of mij letters where ai and aj alternate in the sequence. The matrix of values mij is a Coxeter matrix M = (mij)i,j∈I on I. These groups generalize the braid groups established in 1925 by E. Artin in a natural way and therefore we suggest naming them Artin groups. If one adds the relations ai = 1 to the relations in the presentation ...
متن کاملRigidity of Coxeter Groups and Artin Groups
A Coxeter group is rigid if it cannot be defined by two nonisomorphic diagrams. There have been a number of recent results showing that various classes of Coxeter groups are rigid, and a particularly interesting example of a nonrigid Coxeter group has been given in [17]. We show that this example belongs to a general operation of “diagram twisting”. We show that the Coxeter groups defined by tw...
متن کاملSurface subgroups of Coxeter and Artin groups
We prove that any Coxeter group that is not virtually free contains a surface group. In particular if the Coxeter group is word hyperbolic and not virtually free this establishes the existence of a hyperbolic surface group, and answers in the affirmative a question of Gromov in this setting. We also discuss when Artin groups contain hyperbolic surface groups. 2000 Mathematics Subject Classifica...
متن کاملThe Cayley Graphs of Coxeter and Artin Groups
We obtain a complete classification of the Coxeter and Artin groups whose Cayley graphs with respect to the standard presentations are planar. We also classify those whose Cayley graphs have planar embeddings in which the vertices have no accumulation points.
متن کاملBounded Rank Subgroups of Coxeter Groups, Artin Groups and One-relator Groups with Torsion
We obtain a number of results regarding freeness, quasiconvexity and separability for subgroups of Coxeter groups, Artin groups and one-relator groups with torsion.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1996
ISSN: 0022-4049
DOI: 10.1016/0022-4049(95)00117-4