The problem of recognition of finite simple groups by element orders is solved

Maria A. Grechkoseeva, Alexey M. Staroletov, Andrey V. Vasil'ev

For a finite group $G$, let $\omega (G)$ be the set of element orders of $G$ and let $h(G)$ be the number of pairwise nonisomorphic finite groups $H$ with $\omega (H)=\omega (G)$. We say that the re…