# Isomorphism

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 October 9, 2019, 3:51 pm ad1c9bdddfhttps://brainmass.com/math/linear-transformation/isomorphism-15171

#### Solution Preview

Proof:

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.

$2.19