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Maximal subgroups of the Mathieu group $M_{23}$ and symplectic automorphisms of supersingular K3 surfaces

Shigeyuki Kondo
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Abstract

We show that the Mathieu groups $M_{22}$ and $M_{11}$ can act on the supersingular $K3$ surface with Artin invariant 1 in characteristic 11 as symplectic automorphisms. More generally we show that all maximal subgroups of the Mathieu group $M_{23}$ with three orbits on 24 letters act on a supersingular $K3$ surface with Artin invariant 1 in a suitable characteristic.

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Shigeyuki Kondo. 2005-11-11. Maximal subgroups of the Mathieu group $M_{23}$ and symplectic automorphisms of supersingular K3 surfaces. https://arxiv.org/abs/math/0511286

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