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GroupTheory

  

PCore

  

construct the p-core of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

PCore( p, G )

Parameters

p

-

prime number

G

-

a permutation group

Description

• 

The p-core of a group G is the largest normal p-subgroup of G, where p is a prime integer.  It is equal to the intersection of the Sylow p-subgroups of G, which is, in turn, equal to the core of any one Sylow p-subgroup.

• 

The PCore( p, G ) command constructs the p-core of a group G. The group G must be an instance of a permutation group.

Examples

withGroupTheory:

GDihedralGroup14

GD14

(1)

CPCore2,G

CO2D14

(2)

GroupOrderC

2

(3)

GroupOrderSylowSubgroup2,G

4

(4)

CPCore7,G

CO7D14

(5)

GroupOrderC

7

(6)

Compatibility

• 

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

• 

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

See Also

GroupTheory

GroupTheory[AlternatingGroup]

GroupTheory[Core]

GroupTheory[FittingSubgroup]

GroupTheory[PermutationGroup]

GroupTheory[SylowSubgroup]