On Irreducible, Infinite, Non-affine Coxeter Groups

Mathematics – Group Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

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.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

On Irreducible, Infinite, Non-affine Coxeter Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Irreducible, Infinite, Non-affine Coxeter Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Irreducible, Infinite, Non-affine Coxeter Groups will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-586226

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.