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