Definition:Finite Cyclic Group

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

• Equivalence of Definitions of Finite Cyclic Group

• Results about finite cyclic groups can be found here.