GroupTheory
IsSubnormal
test whether one group is contained as a subnormal subgroup of another
Calling Sequence
Parameters
Description
Examples
Compatibility
IsSubnormal( H, G )
H
-
a group
G
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=G0▹G1▹…▹H
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.
withGroupTheory:
G≔GroupPerm1,2,3,6,4,5,7,8,Perm2,5,6,8
G≔1,2,3,6,4,5,7,8,2,56,8
GroupOrderG
16
H≔SubgroupPerm2,5,6,8,G
H≔2,56,8
IsSubnormalH,G
true
Every normal subgroup of a group is subnormal.
andmapIsSubnormal,NormalSubgroupsG,G
The GroupTheory[IsSubnormal] command was introduced in Maple 2018.
For more information on Maple 2018 changes, see Updates in Maple 2018.
See Also
GroupTheory[IsNormal]
GroupTheory[IsPermutable]
GroupTheory[IsSubgroup]
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