# Category:Definitions/Generators of Groups

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This category contains definitions related to Generators of Groups.

Related results can be found in **Category:Generators of Groups**.

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 3 subcategories, out of 3 total.

### G

## Pages in category "Definitions/Generators of Groups"

The following 13 pages are in this category, out of 13 total.

### G

- Definition:Generated Normal Subgroup
- Definition:Generated Subgroup
- Definition:Generating Set
- Definition:Generator of Cyclic Group
- Definition:Generator of Group
- Definition:Generator of Group/Also denoted as
- Definition:Generator of Group/Also known as
- Definition:Generator of Subgroup
- Definition:Generator of Subgroup/Definition by Predicate
- Definition:Group Presentation