On recognizing the finite simple groups \(L_2(2^m)\) in the class of all groups
Given a group \(G\), let \(\omega(G)\) be the set of all orders of the elements of \(G\). Let \(L_2(q)=\text{PSL}_2(q)\) be the projective special linear group of dimension 2 over the finite field of order \(q=2^m\). Theorem. Let \(G\) be a group and let \(\omega(G)=\omega(L_2(q))\), \(q=2^m>2\). Then \(G\) is isomorphic to \(L_2(q)\). This theorem generalizes a theorem by \textit{W.~Shi} [Adv. Math., Beijing 16, 397-401 (1987; Zbl 0643.20008)].
scientific article; zbMATH DE number 1432165