GroupTheory
Center
construct the center of a group
Calling Sequence
Parameters
Description
Examples
Compatibility
Center( G )
Centre( G )
G
-
a permutation group
The center of a group G is the set of elements of G that commute with all elements of G. That is, an element g of G belongs to the center of G if, and only if, g·x=x·g, for all x in G.
The Center( G ) command constructs the center of a group G. The group G must be an instance of a permutation group, a group defined by a Cayley table, or a custom group that defines its own center method.
The Centre command is provided as an alias.
with⁡GroupTheory:
Whether the center of a dihedral group is trivial or a group of order two depends upon whether the degree is odd or even.
G≔DihedralGroup⁡6
G≔D6
Z≔Center⁡G
Z≔Z⁡D6
GroupOrder⁡Z
2
G≔DihedralGroup⁡7
G≔D7
Z≔Z⁡D7
1
Center⁡AlternatingGroup⁡4
G≔GL⁡3,3
G≔GL3,3
IsAbelian⁡Center⁡G
true
GroupOrder⁡Center⁡G
IsNormal⁡Center⁡G,G
The center of any Frobenius group is trivial.
G≔FrobeniusGroup⁡72,2
G≔2,8,4,73,9,6,5,2,3,4,65,7,9,8,2,43,65,97,8,1,2,43,5,76,8,9,1,3,62,5,84,7,9
GroupOrder⁡Centre⁡G
Likewise, a non-abelian simple group has trivial center.
Centre⁡McLaughlinGroup⁡
Of course, every abelian group is equal to its center.
Centre⁡CyclicGroup⁡24
C24
The GroupTheory[Center] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
See Also
GroupTheory[Centralizer]
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