GroupTheory/IsQuasisimple - Maple Help

GroupTheory

 IsQuasisimple
 determine whether a group is quasi-simple

 Calling Sequence IsQuasisimple( G )

Parameters

 G - a permutation group

Description

 • A group $G$ is quasi-simple if it is perfect and its central quotient is simple. In particular, every simple non-abelian group is quasi-simple.
 • The IsQuasisimple( G ) command returns true if the group G is quasi-simple, and returns false otherwise.

Examples

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

The trivial group is perfect, but its central quotient is itself trivial, hence, not simple.

 > $\mathrm{IsQuasisimple}\left(\mathrm{TrivialGroup}\left(\right)\right)$
 ${\mathrm{false}}$ (1)
 > $\mathrm{IsQuasisimple}\left(\mathrm{Symm}\left(4\right)\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{IsQuasisimple}\left(\mathrm{GL}\left(2,4\right)\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{IsQuasisimple}\left(\mathrm{SL}\left(2,5\right)\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{IsQuasisimple}\left(\mathrm{SL}\left(2,7\right)\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{IsQuasisimple}\left(\mathrm{PerfectGroup}\left(1920,3\right)\right)$
 ${\mathrm{false}}$ (6)
 > $\mathrm{IsQuasisimple}\left(\mathrm{PSO}\left(-1,4,5\right)\right)$
 ${\mathrm{true}}$ (7)