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GroupTheory

  

Core

  

construct the core of a subgroup of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Core( H, G )

Parameters

H

-

a subgroup of G

G

-

a permutation group

Description

• 

If H is a subgroup of a group G, then the core of H in G is the largest normal subgroup of G contained in H.

• 

The Core( H, G ) command computes the core of the subgroup H of the permutation group G.

Examples

withGroupTheory:

GGroupPerm1,2,3,4,5,Perm1,2,3

G1,2,3,4,5,1,2,3

(1)

HSubgroup1,5,4,3,2,G

H1,5,4,3,2

(2)

CCoreH,G

C

(3)

GeneratorsC

(4)

GroupOrderC

1

(5)

GSymmetricGroup4

GS4

(6)

HSubgroupPerm1,2,3,4,Perm1,4,2,3,G

H1,23,4,1,42,3

(7)

CCoreH,G

C1,23,4,1,42,3

(8)

GeneratorsC

1,23,4,1,42,3

(9)

GroupOrderC

4

(10)

Compatibility

• 

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

• 

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

See Also

GroupTheory

GroupTheory[Generators]

GroupTheory[Group]

GroupTheory[GroupOrder]

GroupTheory[PCore]

GroupTheory[Subgroup]

GroupTheory[SymmetricGroup]

Perm