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  3. let g be a group and a be an element of g. let ?:z

Let G be a group and a be an element of G. Let ?:Z?G be...

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Advance Math

Let G be a group and a be an element of G. Let ?:Z?G be a mapdefined by ?(n) =a^{n} for all n?Z. a)Show that ? is a grouphomomorphism. b) Find the image of?, i.e.?(Z), and prove that it isa subgroup ofG.

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