Note on the 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.

Admissible Partitions of Fuzzy Finite State Machines

In this paper we introduce the concept of a covering of a ffsm by another, admissible partitions and relations of a ffsm, μ-orthogonality of admissible partitions, irreducibile ffsm, and the quotient of a ffsm induced by an admissible partition of the state set.