Category:Definitions/Finite Cyclic Groups

This category contains definitions related to Finite Cyclic Groups.
Related results can be found in Category:Finite Cyclic Groups.

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:

$\exists n \in \N: a^n = e$