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

This function finds the largest subgroup of pg in which sg is a normal subgroup. The group sg should be a subgroup of pg.  The result is returned as an unevaluated permgroup call.

The command with(group,normalizer) allows the use of the abbreviated form of this command.

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

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

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

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

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