GroupTheory/RestrictedPermGroup - Maple Help
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GroupTheory

  

RestrictedPermGroup

  

restrict a permutation group to a stable set

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RestrictedPermGroup( G, X )

Parameters

G

-

: PermutationGroup : a permutation group

X

-

: set(posint) : a set of positive integers stable under G

Description

• 

For a permutation group G, and a stable set X of positive integers, the RestrictedPermGroup( G, X ) command returns a permutation group obtained by restricting the action of G to the set X.

• 

The set X must be stable under the action of G; that is, for any element x in X, we must have xg in X, for all g in G. For example, X might be an orbit of G, or a union of orbits of G.

Examples

withGroupTheory:

In this example, an intransitive group is restricted to act on one of its orbits.

GCyclicGroup72,'mindegree'

GC72

(1)

HRestrictedPermGroupG,1,2,3,4,5,6,7,8

H1,2,3,4,5,6,7,8

(2)

The following results in an exception being raised since the set given is not stable under the action of G.

RestrictedPermGroupG,10,11,12,13,14,15

Error, (in Perm:-extPermRestrict) new domain is not fixed set-wise

See Also

GroupTheory

GroupTheory[CyclicGroup]

GroupTheory[Orbit]

GroupTheory[PermRestrict]

GroupTheory[Support]

with