Category:Definitions/Generators of Groups

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 $S$.