Characterization of finite simple group D_n(2)

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.

Keywords

Finite group / simple group / order of element / prime graph

References

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