Inner Automorphisms of Right-angled Coxeter Groups
نویسنده
چکیده
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 Aut(W ). A presentation for Aut◦(W ) was given by Mühlherr in [13]. Our approach is to consider a generating set A obtained as a slight modification of Mühlherr’s. We introduce an effective algorithm for deciding whether a word in the free group F (A) represents an inner automorphism of W under the natural mapping F (A) −→ Aut◦(W ). In other words, we prove the following. Theorem The generalized word problem for Inn(W ) in Aut◦(W ) is solvable.
منابع مشابه
Centralizers of Coxeter Elements and Inner Automorphisms of Right-Angled Coxeter Groups
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 ). Mathematics Subject Classification: 20F10, 20F28, 20F55
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