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.
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