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GroupTheory

  

IsPrimitive

  

determine whether a permutation group is primitive

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsPrimitive( G )

Parameters

G

-

a permutation group

Description

• 

A block for a permutation group G, acting on a set Ω , is a subset B of Ω such that, for all g in G, either Bg=B or Bg and B are disjoint. A block B is trivial if it consists of a single point or if B=Ω . A transitive permutation group G is primitive if it possesses no non-trivial block. Note that an intransitive group is not primitive.

• 

The IsPrimitive( G ) command returns true if the permutation group G is primitive, and returns false otherwise. The group G must be an instance of a permutation group.

Examples

withGroupTheory:

GPermutationGroup1,2,1,2,3,4,5

G1,2,1,2,34,5

(1)

IsPrimitiveG

false

(2)

IsPrimitiveAlternatingGroup4

true

(3)

IsPrimitivePGU3,3

true

(4)

IsPrimitiveDihedralGroup4

false

(5)

IsPrimitiveDihedralGroup5

true

(6)

Compatibility

• 

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

• 

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

See Also

GroupTheory

GroupTheory[IsTransitive]