Stabilizer - Maple Help
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GroupTheory

  

Stabilizer

  

construct the stabilizer of a point, list, or set in a permutation group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Stabilizer( alpha, G )

Stabiliser( alpha, G )

Stabilizer( L, G )

Stabiliser( L, G )

Stabilizer( S, G )

Stabiliser( S, G )

Parameters

G

-

a permutation group

alpha

-

posint; the point whose stabilizer is to be computed

L

-

list(posint); a list of points

S

-

set(posint); a set of points

Description

• 

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

• 

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

• 

The Stabilizer( L, G ) command, where L is a list of points in the domain of the permutation group G, computes the iterated stabilizer of L in G. This is the set of elements of G that fix each point in the list L.

• 

The Stabilizer( S, G ) command, where S is a subset of the domain of the permutation group G, computes the set-wise stabilizer of S in G. This is the set of elements  in  that map the set  to itself, but do not necessarily fix each member of .

• 

The Stabiliser command is provided as an alias.

Examples

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

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]

 


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