construct the centralizer of an element of a group
Centralizer( g, G )
Centraliser( g, G )
a permutation group or a Cayley table group
an element of G
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.
G ≔ Group⁡Perm⁡1,2,Perm⁡1,2,3,4,5
C ≔ Centralizer⁡Perm⁡1,2,3,G
The GroupTheory[Centralizer] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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