English

Finite groups with the same join graph as a finite nilpotent group

Group Theory 2023-06-22 v1

Abstract

Given a finite group G,G, we denote by Δ(G)\Delta(G) the graph whose vertices are the proper subgroups of GG and in which two vertices HH and KK are joined by an edge if and only if G=H,K.G=\langle H,K\rangle. We prove that if there exists a finite nilpotent group XX with Δ(G)Δ(X),\Delta(G)\cong \Delta(X), then GG is supersoluble.

Keywords

Cite

@article{arxiv.2003.12969,
  title  = {Finite groups with the same join graph as a finite nilpotent group},
  author = {Andrea Lucchini},
  journal= {arXiv preprint arXiv:2003.12969},
  year   = {2023}
}
R2 v1 2026-06-23T14:30:42.819Z