GroupTheory
Core
construct the core of a subgroup of a group
Calling Sequence
Parameters
Description
Examples
Compatibility
Core( H, G )
H
-
a subgroup of G
G
a permutation group
If H is a subgroup of a group G, then the core of H in G is the largest normal subgroup of G contained in H.
The Core( H, G ) command computes the core of the subgroup H of the permutation group G.
withGroupTheory:
G≔GroupPerm1,2,3,4,5,Perm1,2,3
G≔1,2,3,4,5,1,2,3
H≔Subgroup1,5,4,3,2,G
H≔1,5,4,3,2
C≔CoreH,G
C≔
GeneratorsC
GroupOrderC
1
G≔SymmetricGroup4
G≔S4
H≔SubgroupPerm1,2,3,4,Perm1,4,2,3,G
H≔1,23,4,1,42,3
C≔1,23,4,1,42,3
1,23,4,1,42,3
4
The GroupTheory[Core] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
See Also
GroupTheory[Generators]
GroupTheory[Group]
GroupTheory[GroupOrder]
GroupTheory[PCore]
GroupTheory[Subgroup]
GroupTheory[SymmetricGroup]
Perm
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