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Def/Cyclic
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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
To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab: Clust/Basic group theory
