I am doing a short paper by Miles and Parmenter "GROUP RINGS WHOSE UNITS FORM A NILPOTENT OR FC GROUP" and the main theorem in that is the following-
Now for (i) or (ii) implies (iii) he writes that it is well known, but I have searched many papers and no where I have seen a result which says that If $U(\mathbb{Z}G)$ is nilpotent/ FC group than $TU(\mathbb{Z}G)$ is a subgroup. Where can I find this result?
Notation- $U(\mathbb{Z}G)$ means group of units of integral group ring $\mathbb{Z}G$ and $TU(\mathbb{Z}G)$ means set of torsion elements in $U(\mathbb{Z}G)$