To which well known group the quotient group $\mathbb R^*/\mathbb{Q}^*$ is isomorphic, where $\mathbb R^*$ is group of non zero reals under multiplication and similarly $\mathbb Q^*$ is group of non-zero rationals under multiplication?
I know that group $\mathbb R^*/\mathbb{Q}^*$ has elements of every order as order of element like $ 2^{\frac{1}{n}} \mathbb Q^* $(left coset) has order $n$. I don't know exactly which group is this. Firstly it comes in my mind the group of complex numbers of mod $1$ but unable to define isomorphism.
Please provide me isomorphic group in a simple way as I don't know group theory in very deep. Thank you.
This is a complete abelian group so it is isomorphic to a cartesian product of copies of the additive group of rational numbers and Prüfer groups.