On the direct product of pure 1, 2, 3 and 4 pure subgroups of Abelian group G - Faez N. Ghaffoori, H. M. A. Abdullah, Saif Z. Hameed (International Journal of Advanced Science and Technology, 2020)
It is well known that study by the pure subgroups and the neat subgroups, by the Fuchs Laszlo [4]. In [8] H.M.A. Abdullah gave some new generalizations of pure subgroups, which are called 1-2 and 3 subgroups of Abelian group G, and in [9], he gave new definition of subgroups which more general of pure subgroups, called pure-4 subgroups. In This paper we shall gave the general case of the results by H.M.A. Abdullah [9]. More ever we are studying some general properties of pure 1, 2, 3 and 4, and use these properties to obtain conditions for direct product of pure -4 subgroups.