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NSE characterization of the Chevalley group \(\varvec{G}_{\varvec{2}} {\varvec{(4)}}\)

Let G be a group and \(\omega (G)=\{o(g)|g\in G\}\) be the set of element orders of G. Let \(k\in \omega (G)\) and \(s_k=|\{g\in G |o(g)=k\}|\). Let \(nse(G)=\{s_k|k\in \omega (G) \}\). In this paper, we prove that if G is a group and \(G_2 (4)\) is the Chevalley group such that \(nse(G)=nse(G_2 (4))\), then \(G\cong G_2 (4)\).