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Note: ~~ means an isomorphism exists. Moreover,if an isomorphism existed from G to G1 I would say G ~~ G1

Questions: If G is an infinite cyclic group, show that G ~~ Z (Z is the set of integers)

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G is an infinite cyclic group, then G=<a>, where a is a generator of G. Now we can define a map f from G to Z as follows:
for any b in G, b=a^i ...

Solution Summary

This is a proof regarding isomorphisms and infinite cyclic groups.