The intersection graph of a finite simple group has diameter at most 5-Reference-Cited by-同舟云学术

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

Published:2021-02-13 Issue:1 Volume:117 Page:1-7
ISSN:0003-889X
Container-title:Archiv der Mathematik
language:en
Short-container-title:Arch. Math.

Author:

Freedman Saul D.^ORCID

Abstract

AbstractLet G be a non-abelian finite simple group. In addition, let

$$\Delta _G$$

Δ G 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

$$\Delta _G$$

Δ G 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.

Funder

St Leonard’s Postgraduate College, University of St Andrews

School of Mathematics & Statistics, University of St Andrews

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00013-021-01583-3.pdf

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