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.

Key words： Finite group; simple group; order of element; prime graph