Given a finite group G, we denote by Δ(G) the graph whose vertices are the proper subgroups of G and in which two vertices H and K are joined by an edge if and only if G = ⟨H, K⟩. We prove that if there exists a finite nilpotent group X with Δ(G) ≅ Δ(X), then G is supersoluble.

中文翻译：

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具有与有限 NILPOTENT 群相同的连接图的有限群

给定一个有限群G, 我们用 Δ(G) 其顶点是的适当子群的图G其中两个顶点H和ķ由边连接当且仅当G= ⟨H,ķ⟩。我们证明如果存在一个有限幂零群X与Δ（G) ≅ Δ(X）， 然后G是超溶解的。