Soft homomorphisms on soft groups

In this paper, we study soft homomorphisms on soft groups and investigate their properties. Given a soft mapping ⟨f,A⟩ from G to Gʹ, we obtain an ordinary map f⌣ from the set SEA(G) of soft elements of G to the set SEA(G′) of soft elements of Gʹ, and show that ⟨f,A⟩ is a soft homomorphism (respectively, soft isomorphism) if and only if f⌣ is an ordinary group homomorphism (respectively, isomorphism). We apply this concept to study soft isomorphism theorems on soft groups. Moreover, we study those soft automorphisms of soft groups and the particular class of soft inner automorphisms. We establish an embedding of the group of soft automorphisms of a soft group G into the group of automorphisms of SEA(G). Furthermore, it is shown that for every soft group G, the soft group of its inner automorphisms is soft isomorphic with the quotient of G by its center ZA(G).