20.6 (2022)

(W. Kimmerle). The prime graph (or Gruenberg–Kegel graph) $\Gamma(X)$ of a group $X$ has vertices labeled by primes appearing as orders of elements in $X$; two distinct primes $p$ and $q$ are adjacent in $\Gamma(X)$ if and only if $X$ contains an element of order $pq$. Denote by $V(\mathbb{Z}G)$ the group of normalized units of the integral group ring of a group $G$. Is it true that for each finite group $G$ the prime graphs of $G$ and $V(\mathbb{Z}G)$ coincide?