ON DIRECT PRODUCT pure − 1 − 2 − 3 SUBGROUPS IN ABELIAN GROUP Gn×Gm

In this paper, we shall define new subgroups which are called pure−1−2−3 in abelian groups Gn×Gm for all n,m∈N which are a family of pure subgroups.

In [1],[2] H.M.A.Abdullah  gave the some general properties of pure− 1−2−3 in abelian group G, but here, we shall prove more than properties on this subgroups in Mod Gn×Gm, which are not valid for pure subgroups.