Saturated fusion systems over $2$-groups

Bob Oliver & Joana Ventura

AMS classification:  Primary 20D20. Secondary 20D45, 20D08

Abstract: 
We develop methods for listing, for a given 2-group $S$, all 
nonconstrained centerfree saturated fusion systems over $S$.  These are 
the saturated fusion systems which could, potentially, include minimal 
examples of exotic fusion systems:  fusion systems not arising from any 
finite group.  To test our methods, we carry out this program over four 
concrete examples:  two of order $2^7$ and two of order $2^{10}$.  Our 
long term goal is to make a wider, more systematic search for exotic fusion 
systems over 2-groups of small order.