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A Coxeter group W is said to be rigid if, given any two Coxeter systems (W, S) and (W, S), there is an automorphism ρ : W −→ W such that ρ(S) = S. We consider the class of Coxeter systems (W, S) for which the Coxeter graph Γ S is complete and has only odd edge labels (such a system is said to be of " type K n "). It is shown that if W has a type K n system,… (More)
If W,S is a right-angled Coxeter system, then Aut W is a semidirect product of the group Aut◦ W of symmetric automorphisms by the automorphism group of a certain groupoid. We show that, under mild conditions, Aut◦ W is a semidirect product of Inn W by the quotient Out◦ W Aut◦ W /Inn W . We also give sufficient conditions for the compatibility of the two… (More)
Let W be a right-angled Coxeter group. We characterize the centralizer of the Coxeter element of a finite special subgroup of W. As an application , we give a solution to the generalized word problem for Inn(W) in Aut(W).
Let W be a right-angled Coxeter group. We demonstrate a practical solution to the generalized word problem for Inn(W) in Aut(W).
Geometric combinatorialists often study partially ordered sets in which each covering relation has been assigned some sort of label. In this article we discuss how each such labeled poset naturally has a monoid, a group, and a cell complex associated with it. Moreover, when the labeled poset satisfies three simple combinatorial conditions, the connections… (More)