GroupTheory
Stabilizer
construct the stabilizer of a point, list, or set in a permutation group
Calling Sequence
Parameters
Description
Examples
Compatibility
Stabilizer( alpha, G )
Stabiliser( alpha, G )
Stabilizer( L, G )
Stabiliser( L, G )
Stabilizer( S, G )
Stabiliser( S, G )
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
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.
The GroupTheory[Stabilizer] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
See Also
GroupTheory[Group]
GroupTheory[GroupOrder]
GroupTheory[IsNormal]
GroupTheory[IsSubgroup]
GroupTheory[SL]
Download Help Document