The intersection graph of a finite simple group has diameter at most 5

Saul D. Freedman

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let G be a non-abelian finite simple group. In addition, let ΔG be the intersection graph of G, whose vertices are the proper non-trivial subgroups of G, with distinct subgroups joined by an edge if and only if they intersect non-trivially. We prove that the diameter of ΔG has a tight upper bound of 5, thereby resolving a question posed by Shen (Czechoslov Math J 60(4):945–950, 2010). Furthermore, a diameter of 5 is achieved only by the baby monster group and certain unitary groups of odd prime dimension.
Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalArchiv der Mathematik
Volume117
Issue number1
Early online date13 Feb 2021
DOIs
Publication statusPublished - Jul 2021

Keywords

  • Intersection graph
  • Simple group
  • Subgroups

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