A nonempty set G is a g-group [with respect to binary operation ∗] if it satisfies the following properties: (g1) ∗ (b c) = (a b) c for all a, b, ∈ G; (g2) each G, there exists an element e such that (e called identity of a); and, (g3) b some eof a. In this study, we gave important properties g-subgroups, homomorphism g-groups, andthe zero element. We also presented couple ways construct g-grou...