GroupTheory
IsCyclic
attempt to determine whether a group is cyclic
Calling Sequence
Parameters
Description
Examples
Compatibility
IsCyclic( G )
G
-
a group
A group G is cyclic if it can be generated by a single element.
The IsCyclic( G ) command attempts to determine whether the group G is cyclic. It returns true if G is cyclic and returns false otherwise. The command may return FAIL on (most) finitely presented groups.
withGroupTheory:
G≔SmallGroup6,1:
IsCyclicG
false
IsCyclicSmallGroup6,2
true
IsCyclicQuasicyclicGroup11
G≔Subgroup481,1627,QuasicyclicGroup3
G≔ℤ3∞
G≔a|a6=1
G≔a∣a6
G≔a,b|a3=b2,b3
G≔a,b∣b3,a-3b2
IsCyclicDirectProductCyclicGroup4,CyclicGroup15
The GroupTheory[IsCyclic] command was introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
See Also
GroupTheory[QuasicyclicGroup]
GroupTheory[SmallGroup]
GroupTheory[Subgroup]
with
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