On Irreducible, Infinite, Non-affine Coxeter Groups
Abstract
The following results are proved: The center of any finite index subgroup of an irreducible, infinite, non-affine Coxeter group is trivial; 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. We also obtain that the orbit of each element other than the identity under the conjugation action in an irreducible, infinite, non-affine Coxeter group is an infinite set. This implies that an irreducible, infinite Coxeter group is affine if and only if it contains an abelian subgroup of finite index.
Cite
@article{arxiv.math/0603670,
title = {On Irreducible, Infinite, Non-affine Coxeter Groups},
author = {Dongwen Qi},
journal= {arXiv preprint arXiv:math/0603670},
year = {2007}
}
Comments
15 pages, the abstract is revised, one corollary and its proof are added in the Introduction, two references added