On Outer Automorphism Groups of Coxeter Groups
نویسنده
چکیده
It is shown that the outer automorphism group of a Coxeter group W of nite rank is nite if the Coxeter graph contains no innnite bonds. A key step in the proof is to show that if the group is irreducible and 1 and 2 any two bases of the root system of W, then 2 = w 1 for some w 2 W. The proof of this latter fact employs some properties of the dominance order on the root system introduced by Brink and Howlett.
منابع مشابه
Compressed Decision Problems for Graph Products and Applications to (outer) Automorphism Groups
It is shown that the compressed word problem of a graph product of finitely generated groups is polynomial time Turing-reducible to the compressed word problems of the vertex groups. A direct corollary of this result is that the word problem for the automorphism group of a right-angled Artin group or a right-angled Coxeter group can be solved in polynomial time. Moreover, it is shown that a res...
متن کاملOn the Direct Indecomposability of Infinite Irreducible Coxeter Groups and the Isomorphism Problem of Coxeter Groups
In this paper we prove that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group, without the finite rank assumption. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group W , the centralizers in W of the normal subgroups of W that are generated by involutions. As a consequence, we show that the problem of deciding ...
متن کاملAutomorphism Groups of Some Affine and Finite Type Artin Groups
We observe that, for fixed n ≥ 3, each of the Artin groups of finite type An, Bn = Cn, and affine type Ãn−1 and C̃n−1 is a central extension of a finite index subgroup of the mapping class group of the (n + 2)-punctured sphere. (The centre is trivial in the affine case and infinite cyclic in the finite type cases). Using results of Ivanov and Korkmaz on abstract commensurators of surface mapping...
متن کاملAutomorphisms of nearly finite Coxeter groups
Suppose that W is an infinite Coxeter group of finite rank n, and suppose that W has a finite parabolic subgroup WJ of rank n 1. Suppose also that the Coxeter diagram of W has no edges with infinite labels. Then any automorphism of W that preserves reflections lies in the subgroup of AutðWÞ generated by the inner automorphisms and the automorphisms induced by symmetries of the Coxeter graph. If...
متن کاملHereditary Conjugacy Separability of Right Angled Artin Groups and Its Applications
We prove that finite index subgroups of right angled Artin groups are conjugacy separable. We then apply this result to establish various properties of other classes of groups. In particular, we show that any word hyperbolic Coxeter group contains a conjugacy separable subgroup of finite index and has a residually finite outer automorphism group. Another consequence of the main result is that B...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996