Omegas of agemos in powerful groups

In this note we show that for any powerful p-group G, the subgroup Ωi(Gpj) is powerfully nilpotent for all i,j≥1 when p is an odd prime, and i≥1, j≥2 when p=2. We provide an example to show why this modification is needed in the case p=2. Furthermore we obtain a bound on the powerful nilpotency class of Ωi(Gpj).