restrict a permutation group to a stable set
RestrictedPermGroup( G, X )
: PermutationGroup : a permutation group
: set(posint) : a set of positive integers stable under G
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.
In this example, an intransitive group is restricted to act on one of its orbits.
G ≔ CyclicGroup⁡72,'mindegree'
H ≔ RestrictedPermGroup⁡G,1,2,3,4,5,6,7,8
The following results in an exception being raised since the set given is not stable under the action of G.
Error, (in Perm:-extPermRestrict) new domain is not fixed set-wise
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