I know that $\Delta_{\Bbb{Z}}(G)$ is the $\Bbb{Z}-$ module generated by elements of form $\{g-1\ \forall\ g\in G\}$. But how do we find them or what it looks like.
I was thinking about finding aug ideal of $\Bbb{Z}S_3$ i.e. $\Delta({S_3})$ and then finding all its powers and what their intersection looks like.
I know that for solvable finite groups $\cap_{i}\Delta^{i}(G)=0$ by a theorem of Roggenkamp.