Indeed, the Monster has no almost simple maximal subgroup with socle $\text{PSL}_2(16)$

Heiko Dietrich; Melissa Lee; Tomasz Popiel

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arXiv · 2310.03317

Indeed, the Monster has no almost simple maximal subgroup with socle $\text{PSL}_2(16)$

Heiko Dietrich·Melissa Lee·Tomasz Popiel

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Abstract

The classification of the maximal subgroups of the Monster $\mathbf{M}$ is believed to be complete subject to an unpublished result of Holmes and Wilson asserting that $\mathbf{M}$ has no maximal subgroups that are almost simple with socle isomorphic to $\text{PSL}_2(8)$, $\text{PSL}_2(16)$, or $\text{PSU}_3(4)$. We prove this result for $\text{PSL}_2(16)$, 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 $\mathbf{M}$.

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Heiko Dietrich, Melissa Lee, Tomasz Popiel. 2023-10-05. Indeed, the Monster has no almost simple maximal subgroup with socle $\text{PSL}_2(16)$. https://arxiv.org/abs/2310.03317

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