GroupTheory
NormalClosure
construct the normal closure of a subgroup or subset of a group
Calling Sequence
Parameters
Description
Examples
Compatibility
NormalClosure( S, G )
NormalClosure( S )
S
-
a subgroup of G or a set of elements of G
G
a permutation group or a Cayley table group
The normal closure of a subset S of a group G is the smallest normal subgroup of G containing S.
The NormalClosure( G ) command constructs the normal closure of S in G.
The group G must be an instance of a permutation group or a Cayley table group.
If S is a subgroup of a group, then the one-argument form NormalClosure( S ) constructs the normal closure of S in the parent group Supergroup( S ).
with⁡GroupTheory:
G≔Alt⁡4
G≔A4
H≔SylowSubgroup⁡3,G
H≔<a permutation group on 4 letters>
GroupOrder⁡H
3
N≔NormalClosure⁡H
N≔1,3,2,1,4,3
GroupOrder⁡N
12
G≔SymmetricGroup⁡3
G≔S3
N≔NormalClosure⁡Perm⁡1,2,G
N≔1,2,2,3
6
GroupOrder⁡NormalClosure⁡Perm⁡1,2,3,G
The GroupTheory[NormalClosure] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
See Also
GroupTheory[IsNormal]
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