Alperin–Brauer–Gorenstein theorem

In mathematics, the Alperin–Brauer–Gorenstein theorem characterizes the finite simple groups with quasidihedral or wreathed Sylow 2-subgroups. These are isomorphic either to three-dimensional projective special linear groups or projective special unitary groups over a finite field of odd order, depending on a certain congruence, or to the Mathieu group $$M_{11}$$. proved this in the course of 261 pages. The subdivision by 2-fusion is sketched there, given as an exercise in, and presented in some detail in.