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GroupTheory

  

Centralizer

  

construct the centralizer of an element of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Centralizer( g, G )

Centraliser( g, G )

Parameters

G

-

a permutation group or a Cayley table group

g

-

an element of G

Description

• 

The centralizer of an element g of a group G is the set of elements of G that commute with g. That is, an element c of G belongs to the centralizer of g if, and only if, g·c=c·g.

• 

The Centralizer( g, G ) command constructs the centralizer of the element g 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 centralizer method.

• 

The centralizer of g in G may also be thought of as the stabilizer of g under the action of G on itself by conjugation.

• 

The Centraliser command is provided as an alias.

Examples

withGroupTheory:

GGroupPerm1,2,Perm1,2,3,4,5

G1,2,1,2,34,5

(1)

CCentralizerPerm1,2,3,G

C1,3,24,5,1,2,3

(2)

GeneratorsC

1,3,24,5,1,2,3

(3)

GroupOrderC

6

(4)

Compatibility

• 

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

• 

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

See Also

GroupTheory

GroupTheory[Center]