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

Research output: Contribution to journalArticlepeer-review

Author(s)

Saul D. Freedman

School/Research organisations

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.
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Details

Original languageEnglish
Number of pages7
JournalArchiv der Mathematik
VolumeFirst Online
Early online date13 Feb 2021
DOIs
Publication statusE-pub ahead of print - 13 Feb 2021

    Research areas

  • Intersection graph, Simple group, Subgroups

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