[2607.28900] Finding 59:29 in the Monster
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arXiv:2607.28900 (math)
[Submitted on 30 Jul 2026]
Title:Finding 59:29 in the Monster
Authors:Heiko Dietrich, Melissa Lee, Anthony Pisani, Aluna Rizzoli<br>View a PDF of the paper titled Finding 59:29 in the Monster, by Heiko Dietrich and 3 other authors
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Abstract:The classification of the maximal subgroups of the Monster group has been completed recently, and explicit generators for each such subgroup (up to conjugacy) have been made available for the software mmgroup, with the exception of the maximal subgroup 59:29, see Dietrich et al. (Adv. Math., 2025; J Algebra, 2026). We provide explicit generators for this last maximal subgroup and comment on the extensive search that led to finding them. Our method is similar to, but significantly more involved than Bray et al.'s (London Math. Soc. J. Comput. Math., 2016) approach for constructing 47:23 in the Baby Monster. Our result allows us to provide a new short proof that the Monster does not have a subgroup PSL2(59), correcting a result of Holmes and Wilson (J. London Math. Soc., 2004).
Subjects:
Group Theory (math.GR)
MSC classes:<br>20D08, 20-08, 20E28
Cite as:<br>arXiv:2607.28900 [math.GR]
(or<br>arXiv:2607.28900v1 [math.GR] for this version)
https://doi.org/10.48550/arXiv.2607.28900
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arXiv-issued DOI via DataCite (pending registration)
Submission history<br>From: Heiko Dietrich [view email]<br>[v1]<br>Thu, 30 Jul 2026 23:43:20 UTC (14 KB)
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