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GroupTheory

  

Center

  

construct the center of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Center( G )

Centre( G )

Parameters

G

-

a permutation group

Description

• 

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.

Examples

withGroupTheory:

GPermutationGroup1,2,1,2,3,4,5

G1,2,1,2,34,5

(1)

CenterG

Z1,2,1,2,34,5

(2)

CenterAlternatingGroup4

ZA4

(3)

GMetacyclicGroup3,4,2

G1,2,34,6,85,7,910,11,12,1,4,10,52,6,11,73,8,12,9

(4)

IsAbelianCenterG

true

(5)

GroupOrderCenterG

12

(6)

IsNormalCenterG,G

true

(7)

Compatibility

• 

The GroupTheory[Center] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

GroupTheory

GroupTheory[Centralizer]