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

Arabian Journal of Mathematics, Sep 2017

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 $$G\cong G_2 (4)$$.

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Maryam Jahandideh Khangheshlaghi, Mohammad Reza Darafsheh. NSE characterization of the Chevalley group $$\varvec{G}_{\varvec{2}} {\varvec{(4)}}$$, Arabian Journal of Mathematics, 2017, 1-6, DOI: 10.1007/s40065-017-0182-4