Abstract
Let G be a finite group, and let π e (G) be the spectrum of G, that is, the set of all element orders of G. In 1987, Shi Wujie put forward the following conjecture. If G is a finite group and M is a non-abelian simple group, then G ≅ M if and only if |G| = |M| and π e (G) = π e (M). In this short paper, we prove that if G is a finite group, then G ≅ M if and only if |G| = |M| and π e (G) = π e (M), where M = D n (2) and n is even.
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Wang, L. Characterization of finite simple group D n (2). Front. Math. China 5, 179–190 (2010). https://doi.org/10.1007/s11464-009-0053-1
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DOI: https://doi.org/10.1007/s11464-009-0053-1