On the direct product of pure 1, 2, 3 and 4 pure subgroups of Abelian group G

Abstract

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.