I've found this exercise.
Determine the elementary divisors of the abelian group in two generators $\{a,b\}$ with the relation $3a=4b$.
I don't see how to solve this. I believe that there should be an explicit way to describe this group, but I couldn't find one. My first thought was that there should be a copy of $\mathbb{Z}$ in this group as each generator has infinite order. And the other factor could be a $\mathbb{Z}_n$.