Definition:Finite Cyclic Group/Definition 2
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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
- 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.