Definition:Generator of Group/Also known as

Generator of Group: Also known as

This is also voiced:

$S$ is a generator of $\struct {G, \circ}$

$S$ generates $\struct {G, \circ}$.

Some sources refer to such an $S$ as a set of generators of $G$, but this terminology is misleading, as it can be interpreted to mean that each of the elements of $S$ is itself a generator of $G$ independently of the other elements.

Other sources use the term generating set, which is less ambiguous.

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 5.3$. Subgroup generated by a subset