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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On subgroups of $ M\sb{24}$. I. Stabilizers of subsets


Author: Chang Choi
Journal: Trans. Amer. Math. Soc. 167 (1972), 1-27
MSC: Primary 20B20
MathSciNet review: 0294472
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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}}$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0294472-0
PII: S 0002-9947(1972)0294472-0
Keywords: Mathieu groups, 5-fold transitive permutation groups, stabilizers of subsets
Article copyright: © Copyright 1972 American Mathematical Society