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GroupTheory

  

NormalClosure

  

construct the normal closure of a subgroup or subset of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

NormalClosure( S, G )

NormalClosure( S )

Parameters

S

-

a subgroup of G or a set of elements of G

G

-

a permutation group or a Cayley table group

Description

• 

The normal closure of a subset S of a group G is the smallest normal subgroup of G containing S.

• 

The NormalClosure( G ) command constructs the normal closure of S in G.

• 

The group G must be an instance of a permutation group or a Cayley table group.

• 

If S is a subgroup of a group, then the one-argument form NormalClosure( S ) constructs the normal closure of S in the parent group Supergroup( S ).

Examples

withGroupTheory:

GAlt4

GA4

(1)

HSylowSubgroup3,G

H<a permutation group on 4 letters>

(2)

GroupOrderH

3

(3)

NNormalClosureH

N1&comma;3&comma;2&comma;1&comma;4&comma;3

(4)

GroupOrderN

12

(5)

GSymmetricGroup3

GS3

(6)

NNormalClosurePerm1&comma;2&comma;G

N1&comma;2&comma;2&comma;3

(7)

GroupOrderN

6

(8)

GroupOrderNormalClosurePerm1&comma;2&comma;3&comma;G

3

(9)

Compatibility

• 

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

• 

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

See Also

GroupTheory

GroupTheory[IsNormal]