The Quillen Complex of Groups of Symplectic Type: The Characteristic 2 Case

Let G = Op′(G) S where S = /pn * T is of symplectic type with T an extra-special p-group and Op′(G) solvable. From results in [[3]] it is easy to show that when p is odd, the Quillen complex of G at p is Cohen-Macaulay. In this note we show that the result also holds when p = 2.