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# Def/Cyclic

Definition of Cyclic (group): Suppose that $G$ is a group. We say that $G$ is cyclic if there exists an element $\gamma \in G$, such that $\gamma$ generates $G$. In other words, $$\forall g \in G, \exists n \in \ZZ, \mbox{ such that } g = \gamma^n.$$

## Logical Connections

This definition logically relies on the following definitions and statements: Def/Group, Def/Generate (group)

The following statements and definitions logically rely on the material of this page: State/Cyclic groups are classified by their order., and State/Groups of prime order are cyclic

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