On Irreducible, Infinite, Non-affine Coxeter Groups

Details On Irreducible, Infinite, Non-affine Coxeter Groups On Irreducible, Infinite, Non-affine Coxeter Groups

2006-03-29

arxiv.org/abs/math/0603670v2

Mathematics

Group Theory

15 pages, the abstract is revised, one corollary and its proof are added in the Introduction, two references added

Scientific paper

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.

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