GroupTheory - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : GroupTheory/Stabilizer

GroupTheory

  

Stabilizer

  

construct the stabilizer of a point in a permutation group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Stabilizer( alpha, G )

Stabiliser( alpha, G )

Parameters

G

-

a permutation group

alpha

-

posint; the point whose stabilizer is to be computed

Description

• 

The stabilizer of a point α under a permutation group G is the set of elements of G that fix α.  It is a subgroup of G. That is, an element g in G belongs to the stabilizer of α if αg=α.

• 

The Stabilizer( alpha, G ) command computes the stabilizer of the point alpha under the action of the permutation group G.

• 

The Stabiliser command is provided as an alias.

Examples

withGroupTheory:

GGroup1,2,4,5

G1,2,4,5

(1)

SStabilizer3,G

S4,5,1,2

(2)

GroupOrderS

4

(3)

GSL3,3

GSL3,3

(4)

SStabilizer1,G

S < a permutation group on 13 letters with 8 generators >

(5)

GroupOrderS

432

(6)

IsSubgroupS&comma;G

true

(7)

IsNormalS&comma;G

false

(8)

Compatibility

• 

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

• 

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

See Also

GroupTheory

GroupTheory[Group]

GroupTheory[GroupOrder]

GroupTheory[IsNormal]

GroupTheory[IsSubgroup]

GroupTheory[SL]