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GroupTheory

  

IsSimple

  

determine whether a group is simple

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsSimple( G )

Parameters

G

-

a group

Description

• 

A group G is simple if it has at least two members, and the only normal subgroups of G are G and the trivial subgroup. Alternatively, the group G is simple if it has no proper homomorphic images.

• 

The IsSimple( G ) command returns true if the group G is simple, and returns false otherwise.

Examples

withGroupTheory:

IsSimpleCyclicGroup7

true

(1)

IsSimpleCyclicGroup12

false

(2)

IsSimpleAlt4

false

(3)

IsSimpleAlt5

true

(4)

IsSimpleAltnassumingn::&apos;posint&apos;,4<n

true

(5)

IsSimplePSL2&comma;2

false

(6)

IsSimplePSL2&comma;3

false

(7)

IsSimplePSL3&comma;3

true

(8)

IsSimplePSLn&comma;qassumingq::primepower,3<q

true

(9)

IsSimpleHaradaNortonGroup

true

(10)

IsSimpleDihedralGroup30

false

(11)

IsSimpleSymm8

false

(12)

IsSimpleOrthogonalGroupO8+(3)

true

(13)

Compatibility

• 

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

• 

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

See Also

GroupTheory

GroupTheory[AlternatingGroup]

GroupTheory[CyclicGroup]

GroupTheory[DihedralGroup]

GroupTheory[HaradaNortonGroup]

GroupTheory[PSL]

GroupTheory[SymmetricGroup]