... This class contains Hattori’s general position class, and also the(aspherical) fiber-type arrangements of Falk and Randell [FR]; see [JP1]. Itfollows from [JP1, Def. 1.8 and Prop. 1.10] and [JP2, ... follows from Proposition 14.Denoting by r and rthe ranks of A and AUrespectively, we know thatbs(M(AU)) = 0, for s ≥ r, and bs(M(A)) =0 ,for s<r.Itfollowsthat p(A,U) <r, ... Hattori’sTheorem 3 [Hat].Randell’s formula for the π-coinvariants of πp(M) ([R1,Th.2 and Prop.9])readily follows from (i), (ii) and (iv). He also raised the question ofπ-freeness for πp(M),...