Two remarks on Wall's D2 problem

Abstract If a finite group G is isomorphic to a subgroup of SO (3), then G has the D2-property. Let X be a finite complex satisfying Wall's D2-conditions. If π 1 ( X ) = G is finite, and χ( X ) ≥ 1 − def( G ), then X ∨ S 2 is simple homotopy equivalent to a finite 2-complex, whose simple homotopy type depends only on G and χ( X ).