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

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

2005-11-11

arxiv.org/abs/math/0511286v1

Mathematics

Algebraic Geometry

7 pages

Scientific paper

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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