group(deprecated)/NormalClosure - Maple Help

group(deprecated)

 NormalClosure
 Find the normal closure of a subgroup of a permutation group

 Calling Sequence NormalClosure(sg, pg)

Parameters

 pg - group in which the normal closure is to be found sg - subgroup of pg

Description

 • Important: The group package has been deprecated. Use the superseding command GroupTheory[NormalClosure] instead.
 • This function finds the smallest normal subgroup of the permutation group pg containing sg. To speed up the computation, it is required that sg be a subgroup of pg. The result is returned as an unevaluated permgroup call.
 • The command with(group,NormalClosure) allows the use of the abbreviated form of this command.

Examples

Important: The group package has been deprecated. Use the superseding command GroupTheory[NormalClosure] instead.

 > $\mathrm{with}\left(\mathrm{group}\right):$
 > $\mathrm{pg}≔\mathrm{permgroup}\left(7,\left\{\left[\left[1,2\right]\right],\left[\left[1,2,3,4,5,6,7\right]\right]\right\}\right):$
 > $\mathrm{sg}≔\mathrm{permgroup}\left(7,\left\{\left[\left[1,2,3\right]\right],\left[\left[3,4,5,6,7\right]\right]\right\}\right):$
 > $\mathrm{NormalClosure}\left(\mathrm{sg},\mathrm{pg}\right)$
 ${\mathrm{permgroup}}{}\left({7}{,}\left\{\left[\left[{1}{,}{2}{,}{3}\right]\right]{,}\left[\left[{3}{,}{4}{,}{5}{,}{6}{,}{7}\right]\right]\right\}\right)$ (1)