Research output: Contribution to journal › Article › peer-review

**The intersection graph of a finite simple group has diameter at most 5.** / Freedman, Saul D.

Research output: Contribution to journal › Article › peer-review

Freedman, SD 2021, 'The intersection graph of a finite simple group has diameter at most 5', *Archiv der Mathematik*, vol. First Online. https://doi.org/10.1007/s00013-021-01583-3

Freedman, S. D. (2021). The intersection graph of a finite simple group has diameter at most 5. *Archiv der Mathematik*, *First Online*. https://doi.org/10.1007/s00013-021-01583-3

Freedman SD. The intersection graph of a finite simple group has diameter at most 5. Archiv der Mathematik. 2021 Feb 13;First Online. https://doi.org/10.1007/s00013-021-01583-3

@article{dc4b8a79a15147c9bb77cbfa51e6a99c,

title = "The intersection graph of a finite simple group has diameter at most 5",

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.",

keywords = "Intersection graph, Simple group, Subgroups",

author = "Freedman, {Saul D.}",

note = "The author was supported by a St Leonard{\textquoteright}s International Doctoral Fees Scholarship and a School of Mathematics & Statistics PhD Funding Scholarship at the University of St Andrews.",

year = "2021",

month = feb,

day = "13",

doi = "10.1007/s00013-021-01583-3",

language = "English",

volume = "First Online",

journal = "Archiv der Mathematik",

issn = "0003-889X",

publisher = "Birkhauser Verlag Basel",

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T1 - The intersection graph of a finite simple group has diameter at most 5

AU - Freedman, Saul D.

N1 - The 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.

PY - 2021/2/13

Y1 - 2021/2/13

N2 - 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.

AB - 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.

KW - Intersection graph

KW - Simple group

KW - Subgroups

U2 - 10.1007/s00013-021-01583-3

DO - 10.1007/s00013-021-01583-3

M3 - Article

VL - First Online

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

ER -

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ID: 272521562