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arXiv · 0706.3911

On the rank of a Coxeter group

Michael L. Mihalik·John G. Ratcliffe
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Abstract

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.

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BibTeXRIS

Michael L. Mihalik, John G. Ratcliffe. 2007-06-26. On the rank of a Coxeter group. https://arxiv.org/abs/0706.3911

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