# Category:Free Groups

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This category contains results about **Free Groups**.

Definitions specific to this category can be found in Definitions/Free Groups.

### Definition 1

A group $G$ is a **free group** if and only if it is isomorphic to the free group on some set.

### Definition 2

A group $G$ is a **free group** if and only if it has a presentation of the form $\gen S$, where $S$ is a set.

That is, it has a presentation without relators.

In this context, **free** means **free of non-trivial relations**.

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