Greedy base sizes for sporadic simple groups

Coen del Valle

doi:10.1515/jgth-2024-0187

Greedy base sizes for sporadic simple groups

Coen del Valle^*

^*Corresponding author for this work

Pure Mathematics

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

Abstract

A base for a permutation group G acting on a set Ω is a sequence ℬ of points of Ω such that the pointwise stabiliser G_ℬ is trivial. Denote the minimum size of a base for G by b(G) There is a natural greedy algorithm for constructing a base of relatively small size; denote by 𝒢(G) the maximum size of a base it produces. Motivated by a longstanding conjecture of Cameron, we determine 𝒢(G) for every almost simple primitive group G with socle a sporadic simple group, showing that 𝒢(G) = b(G) .

Original language	English
Pages (from-to)	1079-1094
Number of pages	16
Journal	Journal of Group Theory
Volume	28
Issue number	5
Early online date	14 Mar 2025
DOIs	https://doi.org/10.1515/jgth-2024-0187
Publication status	Published - 1 Sept 2025

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All about that base
del Valle, C. (Author), Roney-Dougal, C. M. (Supervisor) & Cameron, P. J. (Supervisor), 2 Dec 2025
Student thesis: Doctoral Thesis (PhD)

Cite this

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title = "Greedy base sizes for sporadic simple groups",

abstract = "A base for a permutation group G acting on a set Ω is a sequence ℬ of points of Ω such that the pointwise stabiliser Gℬ is trivial. Denote the minimum size of a base for G by b(G) There is a natural greedy algorithm for constructing a base of relatively small size; denote by 𝒢(G) the maximum size of a base it produces. Motivated by a longstanding conjecture of Cameron, we determine 𝒢(G) for every almost simple primitive group G with socle a sporadic simple group, showing that 𝒢(G) = b(G) .",

author = "{del Valle}, Coen",

note = "Funding: Coen del Valle{\textquoteright}s research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number PGSD-577816-2023, as well as a University of St Andrews School of Mathematics and Statistics Scholarship.",

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N1 - Funding: Coen del Valle’s research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number PGSD-577816-2023, as well as a University of St Andrews School of Mathematics and Statistics Scholarship.

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N2 - A base for a permutation group G acting on a set Ω is a sequence ℬ of points of Ω such that the pointwise stabiliser Gℬ is trivial. Denote the minimum size of a base for G by b(G) There is a natural greedy algorithm for constructing a base of relatively small size; denote by 𝒢(G) the maximum size of a base it produces. Motivated by a longstanding conjecture of Cameron, we determine 𝒢(G) for every almost simple primitive group G with socle a sporadic simple group, showing that 𝒢(G) = b(G) .

AB - A base for a permutation group G acting on a set Ω is a sequence ℬ of points of Ω such that the pointwise stabiliser Gℬ is trivial. Denote the minimum size of a base for G by b(G) There is a natural greedy algorithm for constructing a base of relatively small size; denote by 𝒢(G) the maximum size of a base it produces. Motivated by a longstanding conjecture of Cameron, we determine 𝒢(G) for every almost simple primitive group G with socle a sporadic simple group, showing that 𝒢(G) = b(G) .

U2 - 10.1515/jgth-2024-0187

DO - 10.1515/jgth-2024-0187

M3 - Article

SN - 1433-5883

VL - 28

SP - 1079

EP - 1094

JO - Journal of Group Theory

JF - Journal of Group Theory

IS - 5

ER -

Greedy base sizes for sporadic simple groups

Abstract

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All about that base

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