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)
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).