Abstract:
Let $G$ be a simple group, and let $\omega(G)$ be the set of orders of its elements. It is proved that, if $\omega(G)=\omega(C_p(3))$, where $p$ is an odd prime, then $G\cong C_p(3)$.
Keywords:finite simple group, spectrum of a group, prime graph, recognition by spectrum, symplectic group.