# Generalising right-angled Artin groups

An Artin group $G$ is determined by its Coxeter matrix $M$. This is a symmetric $n \times n$ matrix with entries from $\lbrace 2, 3, \ldots, \infty \rbrace$ that determine the relations between the generators of the group. If all of the entries are in $\lbrace 2, \infty \rbrace$ then we say that $G$ is a right-angled Artin group''.

Is there a name for an Artin group in which all of the entries of its Coxeter matrix are in $\lbrace 2, 3, \infty \rbrace$ (or alternatively $\lbrace 2, 3 \rbrace$)?

Note that, for example, all braid groups are of this type.

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I would think that it is about $(2,3,\infty)$ case. But I have not looked at Crisp-Paris for quite some time. I remember that they embedded every Artin group into one with small type. – Mark Sapir Jun 14 '12 at 11:57
Actually you are right: small type is for exponents $\\{2,3\\}$. – Mark Sapir Jun 14 '12 at 12:31