Definition:Finite Cyclic Group
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Definition
Definition 1
Let $\struct {G, \circ}$ be a cyclic group.
Then $\struct {G, \circ}$ is a finite cyclic group if and only if it is a finite group.
Definition 2
Let $\struct {G, \circ}$ be a cyclic group generated by $a \in G$.
Then $\struct {G, \circ}$ is a finite cyclic group if and only if:
- $\exists n \in \N: a^n = e$
Also see
- Results about finite cyclic groups can be found here.