Gorenstein–Walter theorem explained

In mathematics, the Gorenstein–Walter theorem, proved by, states that if a finite group G has a dihedral Sylow 2-subgroup, and O(G) is the maximal normal subgroup of odd order, then G/O(G) is isomorphic to a 2-group, or the alternating group A₇, or a subgroup of PΓL₂(q) containing PSL₂(q) for q an odd prime power. Note that A₅ ≈ PSL₂(4) ≈ PSL₂(5) and A₆ ≈ PSL₂(9).