A subset of a group is a generating set when every element of is a finite product of elements of and their inverses, equivalently when the subgroup generated by equals .
The rank of a finitely generated group is the minimum cardinality of a generating set of a group of .
Articles by others on the same topic
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).
