Category:Definitions/Infinite Cyclic Group
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This category contains definitions related to the infinite cyclic group.
Related results can be found in Category:Infinite Cyclic Group.
Definition 1
An infinite cyclic group is a cyclic group $G$ such that:
- $\forall n \in \Z_{> 0}: n > 0 \implies \nexists a \in G, a \ne e: a^n = e$
Definition 2
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 $G$.
Pages in category "Definitions/Infinite Cyclic Group"
The following 5 pages are in this category, out of 5 total.