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CyclicGroup

CyclicGroup[n]
represents the cyclic group of degree n.
  • The degree n of CyclicGroup[n] must be a non-negative integer. Degrees 0 and 1 correspond to the trivial or identity group.
  • CyclicGroup[n] is represented by default as a permutation group on the points .
  • Cyclic groups are commutative.
Number of elements of a cyclic group:
Permutation generators of a cyclic group:
Elements of a permutation representation of a cyclic group:
Number of elements of a cyclic group:
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Permutation generators of a cyclic group:
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Elements of a permutation representation of a cyclic group:
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Cyclic groups of degree 0 or 1 are the trivial group, only containing the identity:
In all other cases the cyclic group of degree n contains n elements:
The cyclic group of order n can be represented using the integers with addition modulo n:
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