Fusion systems on \(p\)-groups with an extraspecial subgroup of index \(p\)

In this thesis we classify saturated fusion systems on \(p\)-groups \(S\) containing an extraspecial subgroup of index \(p\) for an arbitrary odd prime \(p\). We prove that if \(F\) is a saturated fusion system on \(S\) with \(O_p(F)\) = 1 then either \(|S|\leq p^6\) or \(S\) is isomorphic to a unique group of order \(p^{p-1}\