Definition:Infinite Cyclic Group/Definition 2

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Definition

An infinite cyclic group is a cyclic group $G$ such that:

$\forall a \in G, a \ne e: \forall m, n \in \Z: m \ne n \implies a^m \ne a^n$

where $e$ is the identity element of $G$.

That is, such that all the powers of $a$ are distinct.


Also see

  • Results about the infinite cyclic group can be found here.


Sources