Skip to content

Research at St Andrews

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

Research output: Contribution to journalArticlepeer-review

Standard

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

In: Archiv der Mathematik, Vol. First Online, 13.02.2021.

Research output: Contribution to journalArticlepeer-review

Harvard

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

APA

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

Vancouver

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

Author

Freedman, Saul D. / The intersection graph of a finite simple group has diameter at most 5. In: Archiv der Mathematik. 2021 ; Vol. First Online.

Bibtex - Download

@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",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

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 -

Related by journal

  1. Characterising bimodal collections of sets in finite groups

    Huczynska, S. & Paterson, M., 9 Jul 2019, (E-pub ahead of print) In: Archiv der Mathematik. First Online, 10 p.

    Research output: Contribution to journalArticlepeer-review

  2. A note on the probability of generating alternating or symmetric groups

    Morgan, L. & Roney-Dougal, C. M., Sep 2015, In: Archiv der Mathematik. 105, 3, p. 201-204 4 p.

    Research output: Contribution to journalArticlepeer-review

  3. Finite groups are big as semigroups

    Dolinka, I. & Ruskuc, N., Sep 2011, In: Archiv der Mathematik. 97, 3, p. 209-217 9 p.

    Research output: Contribution to journalArticlepeer-review

  4. Finite 3-groups of class 3 whose elements commute with their automorphic images

    Abdollahi, A., Faghihi, A., Linton, S. A. & O'Brien, E. A., 2010, In: Archiv der Mathematik. 95, 1, p. 1-7 7 p.

    Research output: Contribution to journalArticlepeer-review

ID: 272521562

Top