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.
FINITE GROUPS with the SAME JOIN GRAPH AS A FINITE NILPOTENT GROUP
Lucchini A.
2021
Abstract
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.File in questo prodotto:
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