Definition:Finite Cyclic Group/Definition 2

Definition

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.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): generator: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): generator: 2.