GroupTheory - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : GroupTheory/IsSupersoluble

GroupTheory

  

IsSupersoluble

  

attempt to determine whether a group is supersoluble

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsSupersoluble( G )

IsSupersolvable( G )

Parameters

G

-

a finite group

Description

• 

A group G is supersoluble if it has a normal series with cyclic quotients. That is, there is a normal series

G=G0G1Gr=1

  

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.

Examples

withGroupTheory:

IsSupersolubleDihedralGroup4

true

(1)

The alternating group of degree 4 is soluble, but is not supersoluble.

IsSupersolubleAlt4

false

(2)

IsSolubleAlt4

true

(3)

Compatibility

• 

The GroupTheory[IsSupersoluble] command was introduced in Maple 2019.

• 

For more information on Maple 2019 changes, see Updates in Maple 2019.

See Also

GroupTheory

GroupTheory[IsSoluble]