منابع مشابه
Irreducible Coxeter Groups
We prove that an infinite irreducible Coxeter group cannot be a non-trivial direct product. Let W be a Coxeter group, and write W = W1 × · · · ×Wp ×Wp+1, where W1, . . . ,Wp are infinite irreducible Coxeter groups, and Wp+1 is a finite one. As an application of the main result, we obtain that W1, . . . ,Wp are unique and Wp+1 is unique up to isomorphism. That is, if W = W̃1 × · · · × W̃q × W̃q+1 i...
متن کاملOn Irreducible, Infinite, Non-affine Coxeter Groups
The following results are proved: (1) The center of any finite index subgroup of an irreducible, infinite, non-affine Coxeter group is trivial; (2) Any finite index subgroup of an irreducible, infinite, non-affine Coxeter group cannot be expressed as a product of two nontrivial subgroups. These two theorems imply a unique decomposition theorem for a class of Coxeter groups. . MSC 2000 Subject C...
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 کاملMinimal Faithful Permutation Degrees for Irreducible Coxeter Groups
The minimal faithful degree of a finite group G, denoted by μ(G), is the least non-negative integer n such that G embeds inside Sym(n). In this article we calculate the minimal faithful permutation degree for all of the irreducible Coxeter groups.
متن کاملEssays on Coxeter groups Coxeter elements in finite Coxeter groups
A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2007
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196707003779