Irreducible Coxeter groups
Group Theory
2007-05-23 v2
Abstract
We prove that a non-spherical irreducible Coxeter group is (directly) indecomposable and that a non-spherical and non-affine Coxeter group is strongly indecomposable in the sense that all its finite index subgroups are (directly) indecomposable. We prove that a Coxeter group has a decomposition as a direct product of indecomposable groups, and that such a decomposition is unique up to a central automorphism and a permutation of the factors. We prove that a Coxeter group has a virtual decomposition as a direct product of strongly indecomposable groups, and that such a decomposition is unique up to commensurability and a permutation of the factors.
Cite
@article{arxiv.math/0412214,
title = {Irreducible Coxeter groups},
author = {Luis Paris},
journal= {arXiv preprint arXiv:math/0412214},
year = {2007}
}