On the rank of a Coxeter group

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dc.creatorMihalik, Michael L.
dc.creatorRatcliffe, John G.
dc.date2007-06-26
dc.date.accessioned2026-07-07T08:12:36Z
dc.date.available2026-07-07T08:12:36Z
dc.descriptionLet 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.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/0706.3911
dc.identifierhttp://arxiv.org/abs/0706.3911
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132510
dc.subjectGroup Theory
dc.subject20F55
dc.titleOn the rank of a Coxeter group
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