Presenting the Baby Monster
type: Item
instance of: scholarly article
title: Presenting the Baby Monster
zbMATH Open document ID: 0797.20018
published in: Journal of Algebra
publication date: 1994-10-19T00:00:00Z
review text: The author studies the so called \(Y_{pqr}\)-groups. A \(Y_{pqr}\)-group is a Coxeter group whose diagram is a \(Y\) with branches of length \(p\), \(q\), \(r\), respectively. The author could show [in Groups, Combinatorics and Geometry, Proc. Durham Symp. 1990, Lond. Math. Soc. Lect. Note Ser. 165, 46-62 (1992)] that \(Y_{555}\) together with an additional relation defines the Bimonster, i.e. the wreath product of the monster group with a group of order two. In this paper the author shows that \(Y_{433}\) together with the additional relation is \(2\times 2 \cdot F_ 2\). Furthermore he gives a new proof of the result mentioned above. The key step in the proof is to investigate the graph \(\Delta\) whose vertices are the \(\{3,4\}\)-transpositions in \(F_ 2\) and whose edges are the pairs \((x,y)\) with \(xy\) a 2-central involution. The main result is that \(\Delta\) is triangulable, i.e. its fundamental group is generated by cycles of length 3. Hence the proof is of the same flavour as the proof for the Bimonster.
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 501079
zbMATH Keywords: bimonster
zbMATH Keywords: triangulable graph
zbMATH Keywords: \(Y_{pqr}\)-groups
zbMATH Keywords: monster group
zbMATH Keywords: \(\{3,4\}\)-transpositions
zbMATH Keywords: 2-central involution
zbMATH Keywords: triangulable
author: Alexander A. Ivanov
reviewed by: Gernot Stroth
MaRDI profile type: Publication
full work available at URL: jabr.1994.1005
OpenAlex ID: W1989204529
DOI: 10.1006/JABR.1994.1005
description: scientific article; zbMATH DE number 501079