20.5 (2022)

(Well-known problem). Let $G$ be a finite group, and $V(\mathbb{Z}G)$ the group of normalized units of the integral group ring of $G$. Do the spectra of $G$ and $V(\mathbb{Z}G)$ coincide? That is, is it true that, for any integer $n$, there is an element of order $n$ in $V(\mathbb{Z}G)$ if and only if there is an element of order $n$ in $G$?