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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