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Calling Sequence
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MathieuGroup( n, formopt )
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Parameters
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n
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an integer in { 9, 10, 11, 12, 21, 22, 23, 24 }
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formopt
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(optional) equation of the form form = F, where F is either "permgroup" (the default) or "fpgroup"
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Description
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The Mathieu groups , for in are a family of transitive permutation groups studied by Émile Mathieu in the late nineteenth century. The simple groups in the family are examples of highly transitive groups. The Mathieu group is simple for in .
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Note that while the Mathieu group of order is simple, it is not sporadic, being isomorphic to the group .
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The MathieuGroup( n ) command returns a permutation group isomorphic to the Mathieu group of degree n, where the degree n must be in { 9, 10, 11, 12, 21, 22, 23, 24 }. This is a sporadic finite simple group for n=11, 12, 22, 23, 24.
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The Mathieu group is, in fact a soluble group.
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The form = F option controls the form of the group returned. By default, a permutation group is returned; this is equivalent to passing the option form = "permgroup". A finitely presented group can be obtained by passing the option form = "fpgroup".
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In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.
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Examples
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>
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C
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1a
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2a
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3a
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4a
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4b
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5a
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8a
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8b
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1
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45
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80
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90
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180
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144
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90
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90
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>
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| (11) |
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Compatibility
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The GroupTheory[MathieuGroup] command was introduced in Maple 17.
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The GroupTheory[MathieuGroup] command was updated in Maple 2020.
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