CyclicGroup( n )
CyclicGroup( n, s )
algebraic; understood to be a positive integer or infinity
(optional) equationof the form form="fpgroup" or form="permgroup" (the default)
A cyclic group is an abelian group generated by a single element. The CyclicGroup command returns a group, either as a permutation group, or a group defined by a generator and a relator, isomorphic to a cyclic group of order n.
By default, a permutation group is returned if n is finite, but you can specify that the cyclic group of order n be constructed as a finitely presented group by passing the option form = "fpgroup".
If n = infinity, then a finitely presented group is returned. It is an error to specify form = permgroup if the argument n is equal to infinity.
You can use the mindegree option to create cyclic permutation groups of much larger order than would be possible without this option. By default, mindegree = false but, if you pass mindegree = true (or just mindegree), then a permutation group of minimal degree which is cyclic of the indicated order is returned.
If n is neither infinity nor a positive integral constant, then a symbolic group representing a cyclic group of order equal to the expression n (which is taken to represent a positive integer) is returned.
In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.
Error, (in GroupTheory:-CyclicGroup) object too large in seq
G ≔ CyclicGroup⁡27⁢37⁢57,':-mindegree'
G ≔ CyclicGroup⁡2⁢k+4
The GroupTheory[CyclicGroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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