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GroupTheory

  

IsNormal

  

test whether one group is contained as a normal subgroup of another

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsNormal( H, G )

Parameters

H

-

a group

G

-

a group

Description

• 

A group H is a normal subgroup of a group G if H is a subgroup of G, and if it is equal to each of its conjugates: H=Hg, for all g in G.

• 

The IsNormal( H, G ) command tests whether the group H is a normal subgroup of the group G.  It returns true if H is normal in G, and returns false otherwise.  For some pairs H and G of groups, the value FAIL may be returned if IsNormal cannot determine whether H is a normal subgroup of G.

Examples

withGroupTheory:

GSymm4

GS4

(1)

HAlt4

HA4

(2)

IsNormalH,G

true

(3)

IsNormalAlt5,G

false

(4)

IsSubgroupAlt5,G

false

(5)

GSymm5

GS5

(6)

HDihedralGroup5

HD5

(7)

IsNormalH,G

false

(8)

IsSubgroupH,G

true

(9)

Compatibility

• 

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

• 

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

See Also

GroupTheory

GroupTheory[AlternatingGroup]

GroupTheory[DihedralGroup]

GroupTheory[IsSubgroup]

GroupTheory[SymmetricGroup]