Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Note on residual finiteness of Artin groups   Let $A$ be an Artin group. A partition $\mathcal{P}$ of the set of standard
generators of $A$ is called admissible if, for all $X,Y \in \mathcal{P}$, $X
\neq Y$, there is at most one pair $(s,t) \in X \times Y$ which has a relation.
An admissible partition $\mathcal{P}$ determines a quotient Coxeter graph
$\Gamma/\mathcal{P}$. We prove that, if $\Gamma/\mathcal{P}$ is either a forest
or an even triangle free Coxeter graph and $A_X$ is residually finite for all
$X \in \mathcal{P}$, then $A$ is residually finite.

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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga