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.

$\mathrm{with}\left(\mathrm{group}\right)\:$

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

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

$\mathrm{NormalClosure}\left(\mathrm{sg}\,\mathrm{pg}\right)$

$\mathrm{permgroup}\left(7\,\left\{\left[\left[1\,2\,3\right]\right]\,\left[\left[3\,4\,5\,6\,7\right]\right]\right\}\right)$