Gorenstein–Walter theorem

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In mathematics, the Gorenstein–Walter theorem, proved by Gorenstein and Walter (1965a, 1965b, 1965c), 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.