Sharpness of saturated fusion systems on a Sylow $p$-subgroup of ${\mathrm{G}}_2(p)$

Valentina Grazian, Ettore Marmo

We prove that the Díaz-Park's sharpness conjecture holds for saturated fusion systems defined on a Sylow $p$-subgroup of the group ${\mathrm{G}}_2(p)$, for $p\ge 5$.