 Generating set of a group

A subset $S$ of a group $G$ is a generating set when every element of $G$ is a finite product of elements of $S$ and their inverses, equivalently when the subgroup $⟨S⟩$ generated by $S$ equals $G$.

A generating set of a group is a subset of the group's elements such that every element of the group can be expressed as a combination of the elements in the generating set using the group's operation (e.g., multiplication, addition).