GroupTheory/IsSubnormal - 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 H is a subnormal  subgroup of a group G if H is a subgroup of G, and if there is a chain

G=G0G1H

  

such that Gk is normal in Gk-1, for each i. 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

withGroupTheory:

GGroupPerm1,2,3,6,4,5,7,8,Perm2,5,6,8

G1,2,3,6,4,5,7,8,2,56,8

(1)

GroupOrderG

16

(2)

HSubgroupPerm2,5,6,8,G

H2,56,8

(3)

IsSubnormalH,G

true

(4)

Every normal subgroup of a group is subnormal.

andmapIsSubnormal,NormalSubgroupsG,G

true

(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]