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

This function determines whether the permutation group sg is a subgroup of the permutation group pg. If it is, then true is returned; otherwise false is returned.

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

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

$\mathrm{pg}≔\mathrm{permgroup}\left(8\,\left\{\left[\left[1\,2\right]\right]\,\left[\left[1\,2\,3\,4\,5\,6\,7\,8\right]\right]\right\}\right)\:$

$\mathrm{sg}≔\mathrm{permgroup}\left(8\,\left\{\left[\left[1\,2\right]\right]\,\left[\left[5\,6\right]\right]\,\left[\left[1\,2\,3\,4\right]\right]\,\left[\left[5\,6\,7\,8\right]\right]\right\}\right)\:$

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

$\mathrm{true}$