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

The intersection of two permutation groups is computed, and returned in the form of a permgroup.

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

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

$\mathrm{pg1}≔\mathrm{permgroup}\left(7\,\left\{\left[\left[2\,3\,4\right]\right]\,\left[\left[3\,4\,5\,6\,7\right]\right]\right\}\right)\:$

$\mathrm{pg2}≔\mathrm{permgroup}\left(7\,\left\{\left[\left[1\,2\right]\right]\,\left[\left[1\,2\,3\,4\,5\,6\right]\right]\right\}\right)\:$

$\mathrm{inter}\left(\mathrm{pg1}\,\mathrm{pg2}\right)$

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