On the rank of a Coxeter group

Details On the rank of a Coxeter group On the rank of a Coxeter group

2007-06-26

arxiv.org/abs/0706.3911v1

Mathematics

Group Theory

21 pages

Scientific paper

Let W be a Coxeter group with Coxeter generators S. The rank of the Coxeter system (W,S) is the cardinality |S| of S. The Coxeter system (W,S) has finite rank if and only if W is finitely generated. If (W,S) has infinite rank, then |S| = |W|, since every element of W is represented by a finite product of elements of S. Thus if W is not finitely generated, the rank of (W,S) is uniquely determined by W. If W is finitely generated, then W may have sets of Coxeter generators S and S' of different ranks. In this paper, we determine the set of all possible ranks for an arbitrary finitely generated Coxeter group W.

Affiliated with

Also associated with

No associations

Rating

On the rank of a Coxeter group 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 the rank of a Coxeter group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the rank of a Coxeter group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-255236