IsNormal - Maple Help
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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  is a normal subgroup of a group  if  is a subgroup of , and if it is equal to each of its conjugates: , for all  in .

• 

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

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(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]

 


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