Forgive me for this question:
Is the trivial group $\{\operatorname{id}\}$ both torsion-free and a torsion group? Or how is the convention here?
By definition (https://en.wikipedia.org/wiki/Torsion-free_abelian_group), a group G is torsion-free if no element other than the identity is of finite order. I would say this is satisfied, since there are no other elements than the identity in $\{\operatorname{id}\}$.
However, Wikipedia states that every finite every abelian is a torsion group, and doesn't exclude $\{\operatorname{id}\}$.
I'm not sure if there is any established convention for the trivial group. Thank you.