GroupTheory/IsSubnormal - Maple Help
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GroupTheory

  

IsSubnormal

  

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

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsSubnormal( H, G )

Parameters

H

-

a group

G

-

a group

Description

• 

A group  is a subnormal  subgroup of a group  if  is a subgroup of , and if there is a chain

  

such that  is normal in , for each . Every normal subgroup of a group is subnormal, but not conversely.

• 

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

Examples

(1)

(2)

(3)

(4)

Every normal subgroup of a group is subnormal.

(5)

Compatibility

• 

The GroupTheory[IsSubnormal] command was introduced in Maple 2018.

• 

For more information on Maple 2018 changes, see Updates in Maple 2018.

See Also

GroupTheory

GroupTheory[IsNormal]

GroupTheory[IsPermutable]

GroupTheory[IsSubgroup]

 


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