Geodesic
FINITE GROUPS WITH THE SAME JOIN GRAPH AS A FINITE NILPOTENT GROUP
Glasgow mathematical journal, Tome 63 (2021) no. 3, pp. 640-650

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DOI

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. 
LUCCHINI, ANDREA. FINITE GROUPS WITH THE SAME JOIN GRAPH AS A FINITE NILPOTENT GROUP. Glasgow mathematical journal, Tome 63 (2021) no. 3, pp. 640-650. doi: 10.1017/S0017089520000415
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     author = {LUCCHINI, ANDREA},
     title = {FINITE {GROUPS} {WITH} {THE} {SAME} {JOIN} {GRAPH} {AS} {A} {FINITE} {NILPOTENT} {GROUP}},
     journal = {Glasgow mathematical journal},
     pages = {640--650},
     year = {2021},
     volume = {63},
     number = {3},
     doi = {10.1017/S0017089520000415},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089520000415/}
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