On irreducible, infinite, nonaffine Coxeter groups

Dongwen Qi. "On irreducible, infinite, nonaffine Coxeter groups." Fundamenta Mathematicae 193.1 (2007): 79-93. <http://eudml.org/doc/282990>.

@article{DongwenQi2007,
abstract = {The following results are proved: The center of any finite index subgroup of an irreducible, infinite, nonaffine Coxeter group is trivial; Any finite index subgroup of an irreducible, infinite, nonaffine 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 prove that the orbit of each element other than the identity under the conjugation action in an irreducible, infinite, nonaffine 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.},
author = {Dongwen Qi},
journal = {Fundamenta Mathematicae},
keywords = {irreducible Coxeter groups; parabolic subgroups; essential elements; CAT(0) spaces; flat torus theorem; solvable subgroup theorem; center; subgroups of finite index},
language = {eng},
number = {1},
pages = {79-93},
title = {On irreducible, infinite, nonaffine Coxeter groups},
url = {http://eudml.org/doc/282990},
volume = {193},
year = {2007},
}

TY - JOUR
AU - Dongwen Qi
TI - On irreducible, infinite, nonaffine Coxeter groups
JO - Fundamenta Mathematicae
PY - 2007
VL - 193
IS - 1
SP - 79
EP - 93
AB - The following results are proved: The center of any finite index subgroup of an irreducible, infinite, nonaffine Coxeter group is trivial; Any finite index subgroup of an irreducible, infinite, nonaffine 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 prove that the orbit of each element other than the identity under the conjugation action in an irreducible, infinite, nonaffine 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.
LA - eng
KW - irreducible Coxeter groups; parabolic subgroups; essential elements; CAT(0) spaces; flat torus theorem; solvable subgroup theorem; center; subgroups of finite index
UR - http://eudml.org/doc/282990
ER -