On Irreducible, Infinite, Non-affine Coxeter Groups
Abstract
Description
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.
15 pages, the abstract is revised, one corollary and its proof are added in the Introduction, two references added
15 pages, the abstract is revised, one corollary and its proof are added in the Introduction, two references added