Definition:Free Group

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Definition

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.


Also see