IsStemGroup - Maple Help

GroupTheory

 IsStemGroup
 attempt to determine whether a group is a stem group

 Calling Sequence IsStemGroup( G )

Parameters

 G - a finite group

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $\mathrm{IsStemGroup}\left(\mathrm{TrivialGroup}\left(\right)\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{IsStemGroup}\left(\mathrm{CyclicGroup}\left(12\right)\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{IsStemGroup}\left(\mathrm{DihedralGroup}\left(4\right)\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{IsStemGroup}\left(\mathrm{DihedralGroup}\left(6\right)\right)$
 ${\mathrm{false}}$ (4)
 > $\mathrm{IsStemGroup}\left(\mathrm{PSL}\left(3,2\right)\right)$
 ${\mathrm{true}}$ (5)

Compatibility

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