Let φ: G --> H be a group homomorphism.
Let φ be a surjection. Then φ is an isomorphism if and only if the order of the element φ(a) is equal to the order of the element a for all a Є G.
Group Homomrphisms and Isomorphisms are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.