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On Subgroups of M24. I: Stabilizers of Subsets

Chang Choi
Transactions of the American Mathematical Society
Vol. 167 (May, 1972), pp. 1-27
DOI: 10.2307/1996123
Stable URL: http://www.jstor.org/stable/1996123
Page Count: 27
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On Subgroups of M24. I: Stabilizers of Subsets
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Abstract

In this paper we study the orbits of the Mathieu group M24 on sets of n points, 1 ≤ n ≤ 12. For n ≥ 6, M24 is not transitive on these sets, so we may classify the sets into types corresponding to the orbits of M24 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 M24 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 M24.

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