The intersection graph of a finite simple group has diameter at most 5
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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.
Freedman , S D 2021 , ' The intersection graph of a finite simple group has diameter at most 5 ' , Archiv der Mathematik , vol. 117 , no. 1 , pp. 1-7 . https://doi.org/10.1007/s00013-021-01583-3
Archiv der Mathematik
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DescriptionThe author was supported by a St Leonard’s International Doctoral Fees Scholarship and a School of Mathematics & Statistics PhD Funding Scholarship at the University of St Andrews.
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