7. Let by the cyclic subgroup of Z15 generated by 3. Show that is isomorphic to Zs. (This requires defining the function o that maps from to Zs and showing that it satisfies the necessary properties.)

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Extracted text: 7. Let <3> by the cyclic subgroup of Z15 generated by 3. Show that <3> is isomorphic to Zs. (This requires defining the function o that maps from <3> to Zs and showing that it satisfies the necessary properties.)