GroupTheory - Maple Programming Help

Online Help

All Products    Maple    MapleSim


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

GroupTheory

  

IsHomocyclic

  

attempt to determine whether a group is homocyclic

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsHomocyclic( G )

Parameters

G

-

a group

Description

• 

A group G is homocyclic if it is isomorphic to a direct power of a cyclic group; that is, of the form Cnk, for some positive integer n and non-negative integer k.

• 

The IsHomocyclic( G ) command attempts to determine whether the group G is homocyclic.  It returns true if G is homocyclic and returns false otherwise. The command may return FAIL on (most) finitely presented groups.

• 

Cyclic groups and elementary abelian groups are homocyclic.

Examples

withGroupTheory:

IsHomocyclicTrivialGroup

true

(1)

IsHomocyclicCyclicGroup15

true

(2)

GSmallGroup36,14:

IsHomocyclicG

true

(3)

AreIsomorphicG,DirectProductCyclicGroup6,CyclicGroup6

true

(4)

IsHomocyclicSmallGroup4,1

true

(5)

IsHomocyclica,b|a2,b2,a·b=b·a

true

(6)

IsHomocyclicSymm3

false

(7)

IsHomocyclicQuaternionGroup

false

(8)

Compatibility

• 

The GroupTheory[IsHomocyclic] command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

GroupTheory

GroupTheory[AreIsomorphic]

GroupTheory[CyclicGroup]

GroupTheory[DirectProduct]

GroupTheory[IsCyclic]

GroupTheory[QuaternionGroup]

GroupTheory[SmallGroup]

GroupTheory[SymmetricGroup]

GroupTheory[TrivialGroup]

with