On irreducible, infinite, nonaffine Coxeter groups

Tom 193 / 2007

Dongwen Qi Fundamenta Mathematicae 193 (2007), 79-93 MSC: Primary 20F55; Secondary 20F65, 57M07, 53C23. DOI: 10.4064/fm193-1-5

Streszczenie

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.

Autorzy

  • Dongwen QiDepartment of Mathematics
    The Ohio State University
    231 West 18th Avenue
    Columbus, OH 43210, U.S.A.
    e-mail

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