Edited by Martin W. Liebeck
Edited by Jan Saxl
Publisher: Cambridge University Press
Print Publication Year: 1992
Online Publication Date:September 2010
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511629259.008
We complete the proof that Y555 is a presentation of the Bimonster.
Recently the author published a paper which showed how progress had been made towards proving that Y555 (which we redefine below) is a presentation for the wreath square of the Fischer-Griess Monster (which we call the Bimonster) and outlined a possible method of completing the proof. Since then the proof has indeed been completed, but by a different method: results announced by A. Ivanov at the 1990 Durham Conference, proved by showing the simple connectedness of a certain simplicial complex, meant that a slight strengthening of the results of was sufficient to complete the proof. This was achieved during the conference, and it therefore seems appropriate to publish it here in the conference proceedings.
We also take the opportunity to present proofs of two other results needed for which no full published version currently exists.
We start by recalling some of the notation, terminology and (without proof) results of. Note that the numbering of the theorems has been changed. References contain many other useful results about subgroups of Y555.
We recall that a Coxeter group is generated by involutions corresponding to the nodes of a (Coxeter) diagram. The product of two generators has order 2 or 3 according as the corresponding nodes are unjoined or joined by a single unlabelled edge. (Other product orders are possible and correspond to other types of join.)
Part 1 - Sporadic groups
Part 2 - Moonshine
Part 3 - Local and geometric methods in group theory
Part 4 - Geometries and related groups
Part 5 - Finite and algebraic groups of Lie type
Part 6 - Finite permutation groups
Part 7 - Further aspects of simple groups
Part 8 - Related topics