On irreducible, infinite, nonaffine Coxeter groups

• Autorzy: Dongwen Qi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 20F65: Geometric group theory
• 20F55: Reflection and Coxeter groups
• 53C23: Global geometric and topological methods (\`a la Gromov); differential geometric analysis on metric spaces
• 57M07: Topological methods in group theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 193
• Numer: 1
• Strony: 79-93

Daty

wydano

2007

Twórcy

autor

Dongwen Qi

• Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, U.S.A.

Identyfikatory

DOI

10.4064/fm193-1-5