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 $2$.
@article{10_37236_4298,
author = {John Ballantyne and Peter Rowley},
title = {Local fusion graphs and sporadic simple groups.},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {3},
doi = {10.37236/4298},
zbl = {1330.20027},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4298/}
}
TY - JOUR
AU - John Ballantyne
AU - Peter Rowley
TI - Local fusion graphs and sporadic simple groups.
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/4298/
DO - 10.37236/4298
ID - 10_37236_4298
ER -
%0 Journal Article
%A John Ballantyne
%A Peter Rowley
%T Local fusion graphs and sporadic simple groups.
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/4298/
%R 10.37236/4298
%F 10_37236_4298
John Ballantyne; Peter Rowley. Local fusion graphs and sporadic simple groups.. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/4298
