SOME REMARKS ON SUBGROUPS DETERMINED BY CERTAIN IDEALS IN INTEGRAL GROUP-RINGS

Let G be a group, ZG the integral group ring of G and I(G) its augmentation ideal. Subgroups determined by certain ideals of ZG contained in I(G) are identified. For example, when G = HK, where H, K are normal subgroups or G and H and K subset-or-equal-to zeta (H), then the subgroups or G determined by I(G)I(H)I(G), and I3(G)I(H) are obtained. The subgroups of any group G with normal subgroup H determined by (i) I2(G)I(H) + I(G)I(H)I(G) + I(H)I2(G), when H' subset-or-equal-to [H, G, G] and (ii) I(G)I(H)I(G) when deg H-2(G/H', T) less-than-or-equal-to 1, are computed. The subgroup of G determined by I(n)(G) + I(G)I(H) when H is a normal subgroup of G with G/H free Abelian is also obtained