$\mathbb{Z}$ has no torsion? What does is mean to say that $\mathbb{Z}$ has no torsion? 
This is an important fact for any course?
Thanks, I heard that in my field theory course, but I don't know what it is. 

@d555, you might want to know that the notion of torison is extremely important, for example if $A$ is finitely generated and abelian group, then it can be written as the direct sum of its torsion subgroup $T(A)$ and a torsion-free subgroup (but this is not true for all infinitely generated abelian groups). $T(A)$ is uniquely determined.
