construct the stabilizer of a point, list, or set in a permutation group
Stabilizer( alpha, G )
Stabiliser( alpha, G )
Stabilizer( L, G )
Stabiliser( L, G )
Stabilizer( S, G )
Stabiliser( S, G )
a permutation group
posint; the point whose stabilizer is to be computed
list(posint); a list of points
set(posint); a set of points
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 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 g in G that map the set S to itself, but do not necessarily fix each member of S.
The Stabiliser command is provided as an alias.
G ≔ Group⁡1,2,4,5
S ≔ Stabilizer⁡3,G
G ≔ SL⁡3,3
S ≔ Stabilizer⁡1,G
S ≔ Stabilizer⁡1,7,3,11,G
S ≔ Stabilizer⁡1,2,G
S≔ < a permutation group on 13 letters with 4 generators >
The GroupTheory[Stabilizer] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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