# Category:Infinite Cyclic Group

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This category contains results about **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 $G$.

## Subcategories

This category has only the following subcategory.

### A

## Pages in category "Infinite Cyclic Group"

The following 6 pages are in this category, out of 6 total.