attempt to determine whether a group is supersoluble
IsSupersoluble( G )
IsSupersolvable( G )
a finite group
A group G is supersoluble if it has a normal series with cyclic quotients. That is, there is a normal series
with each subgroup Gi normal in G, and for which each of the quotients GiGi+1 is cyclic.
It follows that every supersoluble group is soluble but, as the examples below illustrate, the converse is not true.
The IsSupersoluble( G ) command attempts to determine whether the finite group G is supersoluble. It returns true if G is supersoluble and returns false otherwise.
The IsSupersolvable( G ) command is provided as an alias.
The alternating group of degree 4 is soluble, but is not supersoluble.
Direct products of supersoluble groups are supersoluble.
G ≔ DirectProduct⁡SearchSmallGroups⁡'supersoluble','order'=10..20,'form'=permgroup
G≔ < a permutation group on 558 letters with 92 generators >
The GroupTheory[IsSupersoluble] command was introduced in Maple 2019.
For more information on Maple 2019 changes, see Updates in Maple 2019.
Download Help Document
What kind of issue would you like to report? (Optional)