Rewriting Systems and the Complete Growth Series for Triangular Coxeter Groups

M. D. Mamaghani

Allameh Tabatabaii University

Abstract: In this paper, a complete finite rewriting system is constructed for Coxeter groups of the form
$$ W=\langle a,b,c\mid a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=1\rangle $$
with respect to the system of generators $S=\{a,b,c\}$, where $p,q,r\in \mathbb Z$, $p,q,r\ge 2$ and $1/p+1/q+1/r<1$. Rewriting systems of this kind can be used to evaluate the complete growth series of a group.

UDC: 512.54

Received: 20.12.2000

DOI: 10.4213/mzm357

 English version: Mathematical Notes, 2002, 71:3, 392–399

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