Local Fusion Graphs and Sporadic Simple Groups

  • John Ballantyne
  • Peter Rowley
Keywords: Local Fusion Graph, Sporadic Simple Group, Diameter

Abstract

For a group $G$ with $G$-conjugacy class of involutions $X$, the local fusion graph $\mathcal{F}(G,X)$ has $X$ as its vertex set, with distinct vertices $x$ and $y$ joined by an edge if, and only if, the product $xy$ has odd order. Here we show that, with only three possible exceptions, for all pairs $(G,X)$ with $G$ a sporadic simple group or the automorphism group of a sporadic simple group, $\mathcal{F}(G,X)$ has diameter $2$.
Published
2015-07-31
Article Number
P3.18