Let G be a group and g E G. Show that Ø:Z→G by Ø(n) = g" is a homomorphism and isomorphism.
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- 14. Let be an abelian group of order where and are relatively prime. If and , prove that .Label each of the following statements as either true or false. Let x,y, and z be elements of a group G. Then (xyz)1=x1y1z1.If G is a cyclic group, prove that the equation x2=e has at most two distinct solutions in G.