FINITE GROUPS WITH THE SAME JOIN GRAPH AS A FINITE NILPOTENT GROUP

Abstract

AbstractGiven 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.