# Group Homomrphisms and Isomorphisms

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Let Î¦: G --> H be a group homomorphism.

Let Î¦ be a surjection. Then Î¦ 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 Ñ”G.

See the attached file.

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#### Solution Summary

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

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