Some \(Y\)-groups
type: Item
instance of: scholarly article
title: Some \(Y\)-groups
zbMATH Open document ID: 0871.20010
DOI: 10.1023/A:1004964605735
published in: Geometriae Dedicata
publication date: 1997-10-01T00:00:00Z
review text: A \(Y\)-group is a group which is a factorgoup of a Coxeter group whose diagram has the shape of a \(Y\) with arms of length \(p,q,r\in\mathbb{N}\), also denoted by a \(Y_{pqr}\)-group. The most famous one might be the \(Y_{555}\)-group with the one additional relation \((ab_1c_1ab_2c_2ab_3c_3)^{10}=1\) which has been proved to be the bimonster by \textit{S. Norton} [Lond. Math. Soc. Lect. Note Ser. 165, 63-76 (1992; Zbl 0806.20019)] and \textit{A. Ivanov} [J. Algebra 163, No. 1, 88-108 (1994; Zbl 0797.20018)]. The author investigates the cases \(1=r\), \(1\leq p\leq 5\), \(q\leq 4\) and \(2=r\leq q\leq p\leq 5\), \(q\leq 3\) except \(pqr=532\). These groups are all related to some groups generated 3-transpositions. This basically is the idea of the proof. The author shows that the \(Y\)-presentation yields a so called Fischerian presentation which then can be used to identify the groups. Due to this fact no computer application is needed.
reviewed by: Gernot Stroth
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F55
zbMATH DE Number: 1003880
zbMATH Keywords: Coxeter groups
zbMATH Keywords: groups generated 3-transpositions
zbMATH Keywords: \(Y\)-presentations
zbMATH Keywords: Fischer presentations
author: Marguerite-Marie Virotte-Ducharme
MaRDI profile type: Publication
full work available at URL: a:1004964605735
OpenAlex ID: W74279460
description: scientific article; zbMATH DE number 1003880