My question is:
Are there currently any classification (up to isomorphism) of infinite abelian groups having no non-trivial finite subgroup?
It seems many have asked whether an infinite group can have all proper subgroup being finite, but few are interested in the infinite groups without any non-trivial finite subgroup.
I know such group is equivalent to that no non-trivial element is of finite order and the basic examples are $\mathbb{Z}, \mathbb{Q}, \mathbb{R}, \mathbb{C}$ and their direct sums, with addition (+) as the group operation. However, what are the other examples and do we know everything about them?
Thanks.