Originally Posted by

**DanielThrice** So here was my initial postulate:

Show that Q/Z is isomorphic to the multiplicative group U∗ consisting of all roots of unity in C. (That is, U∗ = {z ∈ C|zn= 1 for some n ∈ Z+}.)

This is what I understand:

I know I probably need to use the first isomorphism/homomorphism theorem, which states that if you have a homomorphism f from G to G', then there is an isomorphism from the quotient group G/H to the image f(G), where H = Ker f.

So the idea is to exhibit a homomorphism between Q and U* whose kernel is precisely the integers. To do this, we first figure out what the identity in U* is (because we need to show that our eventual homomorphism takes the integers to this identity in U*).

Any thoughts on this problem?