Abstract
Let ZG be the integral group ring of a group G, and I(G) its augmentation ideal. For a free group F and a subgroup R of F, the intersections I-3 (F) boolean AND I-2 (R) and I-3(F) boolean AND I(R) are determined. For an arbitrary group G and a subgroup H of G, the subgroup G boolean AND (1 + I-2(G)I(H)) is identified when either H/H' or G/HG' is torsion-free. Also, when S is another subgroup of F and R is normal in F, the subgroup F boolean AND (I + ZFI(2) (R)I(S)) of F is identified.