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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 ΓS is complete and has only odd edge labels (such a system is said to be of “type Kn”). It is shown that if W has a type Kn system, then(More)
If (W, S) is a right-angled Coxeter group, 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(More)
approved: William A. Bogley 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 of W which carries S to S ′ In this dissertation we review rigidity results of D. Radcliffe [29] and of R. Charney and M. Davis [11], noting that certain restrictions must be placed on the Coxeter group in order(More)
If W is a right-angled Coxeter group, then the group Aut(W ) of automorphisms of W acts on the set of conjugacy classes of involutions in W. Following Tits [16], the kernel of this action is denoted by Aut◦(W ). Since W is a CAT(0) group [12], the index of Aut◦(W ) in Aut(W ) is finite and there is a series 1 Inn(W ) Aut◦(W ) Aut(W ) of normal subgroups of(More)
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