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GroupTheory

  

MathieuGroup

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

MathieuGroup(n)

Parameters

n

-

an integer in { 9, 10, 11, 12, 21, 22, 23, 24 }

Description

• 

The Mathieu groups Mn, for n in 9,10,11,12,21,22,23,24 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 Mn is simple for n in 11,12,21,22,23,24.

• 

Note that the Mathieu group M21 of order 20160 is simple, but is not sporadic, being isomorphic to the group PSL3,4 .

• 

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.

Examples

withGroupTheory:

MathieuGroup11

M11

(1)

GroupOrderMathieuGroup23

10200960

(2)

GMathieuGroup12

G:=M12

(3)

DegreeG

12

(4)

Compatibility

• 

The GroupTheory[MathieuGroup] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

GroupTheory[Degree]

GroupTheory[GroupOrder]

GroupTheory[IsTransitive]

 


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