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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)
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