Presenting the Baby Monster
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.
scientific article; zbMATH DE number 501079