GroupTheory/RestrictedPermGroup - Maple Help
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GroupTheory

 RestrictedPermGroup
 restrict a permutation group to a stable set

 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 ${x}^{g}$ in $X$, for all $g$ in $G$. For example, $X$ might be an orbit of $G$, or a union of orbits of $G$.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$

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

 > $G≔\mathrm{CyclicGroup}\left(72,'\mathrm{mindegree}'\right)$
 ${G}{≔}{{C}}_{{72}}$ (1)
 > $H≔\mathrm{RestrictedPermGroup}\left(G,\left\{1,2,3,4,5,6,7,8\right\}\right)$
 ${H}{≔}⟨\left({1}{,}{2}{,}{3}{,}{4}{,}{5}{,}{6}{,}{7}{,}{8}\right)⟩$ (2)

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

 > $\mathrm{RestrictedPermGroup}\left(G,\left\{10,11,12,13,14,15\right\}\right)$

 See Also