21.94 (2026)

The Gruenberg–Kegel graph (or the prime graph) $GK(G)$ of a finite group $G$ is a labelled graph with vertex set consisting of all prime divisors of the order of $G$ in which different vertices $p$ and $q$ are adjacent if and only if $G$ contains an element of order $pq$. Let $\overline{GK}(G)$ denote the abstract graph obtained from $GK(G)$ by removing all labels. A finite group $G$ is said to be recognizable by the isomorphism type of its Gruenberg–Kegel graph if there are no finite groups $H \not\cong G$ with $\overline{GK}(H)$ isomorphic to $\overline{GK}(G)$.

Are there infinitely many (pairwise non-isomorphic) finite groups which are recognizable by the isomorphism type of the Gruenberg–Kegel graph?