Finite groups · Family
Finite cyclic groups
One cyclic group for every finite order n.
Reference coverageFinite families
Parameter domain
One cyclic group for every finite order n.
| Parameter | Allowed values |
|---|---|
| n | positive integer |
Reference properties
Conventions and use
Ordinary complex irreducibles are the one-dimensional characters χₖ(a) = exp(2πik/n), with k taken modulo n. [sources]
Names and aliases
Z/nZ · ℤₙ
Claims and sources
Each assertion has a stable identifier within this record and a source locator or derivation. Cite the dataset edition when referring to a corrected or historical claim.
Definition
The group generated by a with relation aⁿ = 1, with a of exact order n.
family:finite-cyclic#definitionParameter domain
n: positive integer
family:finite-cyclic#parametersScope and restrictions
One cyclic group for every finite order n.
family:finite-cyclic#restrictionConventions and use
Ordinary complex irreducibles are the one-dimensional characters χₖ(a) = exp(2πik/n), with k taken modulo n.
- GAP · Characters and symmetrizationsOrdinary character tables and irreducible charactersOpen source
family:finite-cyclic#conventions-1