Abstract:
The spectrum of a group is the set of its element orders. Let $L=PSL_n(q)$, where $n$ is a prime greater than $3$. We show that every finite group whose spectrum is the same as the spectrum of $L$ is isomorphic to an extension of $L$ by a subgroup of the outer automorphism group of $L$.
Keywords:simple linear group, prime graph, quasirecognizability by spectrum.