Abstract:
As shown in [1] the simple group $^2D_{2m+1}(3)$ is recognizable by spectrum. The main result of this paper generalizes the above, stating that $^2D_{2m+1}(3)$ is recognizable by prime graph. In other words, we show that if $G$ is a finite group satisfying $\Gamma(G)=\Gamma(^2D_{2m+1}(3))$ then $G\cong^2D_{2m+1}(3)$.
Keywords:recognition, prime graph, simple group, spectrum, element order.
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