Some remarks on goursat lemma

In this article,we give a characterization of containment of subgroups in a direct product A\times B\times C. Other potential generalizations are investigated and applications characterizing different types of groups and modules are given. Most of applications are simple while somewhat deeper applications occur in the case of cyclic modules.

Keywords:

Goursat Lemma , Groups , Permutable subgroups , Cyclic modules