Indeed, the Monster has no almost simple maximal subgroup with socle PSL₂(16)

2023/10/05 by Heiko Dietrich, Melissa Lee, Dietrich, Heiko +3
Mathematics · Medicine · #Chronic Lymphocytic Leukemia Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2310.03317

openalex publication_date 2023/10/05 · openalex created_date 2023/10/09 · openalex updated_date 2026/07/28

Abstract

The classification of the maximal subgroups of the Monster M is believed to be complete subject to an unpublished result of Holmes and Wilson asserting that M has no maximal subgroups that are almost simple with socle isomorphic to PSL₂(8), PSL₂(16), or PSU₃(4). We prove this result for PSL₂(16), with the intention that the other two cases will be dealt with in an expanded version of this paper. Our proof is supported by reproducible computations carried out using Seysen's publicly available Python package mmgroup for computing with M.

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