 GroupTheory/IsAlmostSimple - Help

GroupTheory

 IsAlmostSimple
 determine whether a group is almost simple

 Calling Sequence IsAlmostSimple( G )

Parameters

 G - a permutation group

Description

 • A group $G$ is almost simple if it has an unique minimal normal subgroup which is a non-Abelian simple group. Alternatively, the group $G$ is almost simple if, up to isomorphism, we have $S\le G$ and $G\le \mathrm{Aut}\left(S\right)$, for a non-Abelian simple group $S$.
 • The IsAlmostSimple( G ) command returns true if the group G is almost simple, and returns false otherwise.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $\mathrm{IsAlmostSimple}\left(\mathrm{Symm}\left(3\right)\right)$
 ${\mathrm{false}}$ (1)
 > $\mathrm{IsAlmostSimple}\left(\mathrm{Symm}\left(4\right)\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{IsAlmostSimple}\left(\mathrm{Symm}\left(5\right)\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{IsAlmostSimple}\left(\mathrm{PSL}\left(2,5\right)\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{IsAlmostSimple}\left(\mathrm{CyclicGroup}\left(11\right)\right)$
 ${\mathrm{false}}$ (5)

Compatibility

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