On subgroups of 𝑀₂₄. I. Stabilizers of subsets

Choi, Chang

doi:10.1090/S0002-9947-1972-0294472-0

On subgroups of $M_{24}$. I. Stabilizers of subsets
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Trans. Amer. Math. Soc. 167 (1972), 1-27 Request permission

Abstract:

In this paper we study the orbits of the Mathieu group ${M_{24}}$ on sets of n points, $1 \leqq n \leqq 12$. For $n \geqq 6,{M_{24}}$ is not transitive on these sets, so we may classify the sets into types corresponding to the orbits of ${M_{24}}$ and then show how to construct a set of each type from smaller sets. We determine the stabilizer of a set of each type and describe its representation on the 24 points. From the conclusions, the class of subgroups which are maximal among the intransitives of ${M_{24}}$ can be read off. This work forms the first part of a study which yields, in particular, a complete list of the primitive representations of ${M_{24}}$.

References

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Die

fach transitiven Gruppen von Mathieu

12