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GroupTheory

  

NormalSubgroups

  

compute the normal subgroups of a finite group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

NormalSubgroups( G )

Parameters

G

-

a finite group

Description

• 

The NormalSubgroups( G ) command computes the normal subgroups of a finite group G.

• 

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

Examples

withGroupTheory:

GAlt4

GA4

(1)

SNormalSubgroupsG

S1,3,2,1,4,3,1,32,4,1,42,3,

(2)

andmapIsNormal,S,G

true

(3)

The alternating group of degree 5 is simple, so it has only two normal subgroups, itself and the trivial subgroup.

GAlt5

GA5

(4)

NormalSubgroupsG

,A5

(5)

The automorphism group of the Clebsch graph contains a perfect normal subgroup of index two.

useGraphTheoryinAAutomorphismGroupSpecialGraphs:-ClebschGraph;GroupOrderA;NANormalSubgroupsA;GroupOrderNA2;IsPerfectNA2end use

true

(6)

Compatibility

• 

The GroupTheory[NormalSubgroups] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

GroupTheory

GroupTheory[IsNormal]