# Category:Generators

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This category contains results about Generators in the context of Group Theory.

Definitions specific to this category can be found in Definitions/Generators.

Let $\struct {G, \circ}$ be a group.

Let $S \subseteq G$.

Then **$S$ is a generator of $G$**, denoted $G = \gen S$, if and only if $G$ is the subgroup generated by $S$.

## Subcategories

This category has the following 2 subcategories, out of 2 total.