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Group Homomrphisms and Isomorphisms

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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 єG.

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Solution Summary

Group homomrphisms and isomorphisms are investigated and discussed in the solution. The solution is detailed and well presented.