construct the center of a group
Center( G )
Centre( 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.
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
Z ≔ Center⁡G
G ≔ DihedralGroup⁡7
G ≔ GL⁡3,3
The center of any Frobenius group is trivial.
G ≔ FrobeniusGroup⁡72,2
G≔ < a permutation group on 9 letters with 5 generators >
Likewise, a non-abelian simple group has trivial center.
Of course, every abelian group is equal to its center.
The GroupTheory[Center] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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