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)© BrainMass Inc. brainmass.com September 21, 2018, 12:30 pm ad1c9bdddf - https://brainmass.com/math/linear-transformation/isomorphism-15171
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 ...
This is a proof regarding isomorphisms and infinite cyclic groups.