A group $G$ is a stem group if its center is contained in its derived subgroup. Stem groups are minimal order groups within their isoclinism class.

The IsStemGroup( G ) command attempts to determine whether the group G is a stem group. It returns true if G is a stem group and returns false otherwise.

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

$\mathrm{IsStemGroup}\left(\mathrm{TrivialGroup}\left(\right)\right)$

$\mathrm{true}$

$\mathrm{IsStemGroup}\left(\mathrm{CyclicGroup}\left(12\right)\right)$

$\mathrm{false}$

$\mathrm{IsStemGroup}\left(\mathrm{DihedralGroup}\left(4\right)\right)$

$\mathrm{true}$

$\mathrm{IsStemGroup}\left(\mathrm{DihedralGroup}\left(6\right)\right)$

$\mathrm{false}$

$\mathrm{IsStemGroup}\left(\mathrm{PSL}\left(3\,2\right)\right)$

$\mathrm{true}$

The GroupTheory[IsStemGroup] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.