text: Infinite groups can also have finite generating sets. The additive group of integers has 1 as a generating set. The element 2 is not a generating set, as the odd numbers will be missing. The two-element subset  is a generating set, since  (in fact, any pair of coprime numbers is, as a consequence of Bézout's identity).
  The dihedral group of an n-gon (which has order ) is generated by the set , where  represents rotation by  and  is any reflection across a line of symmetry.
  The cyclic group of order , , and the th roots of unity are all generated by a single element (in fact, these groups are isomorphic to one another).
  A presentation of a group is defined as a set of generators and  a collection of relations between them, so any of the examples listed on that page contain examples of generating sets.
  Free group
  The most general group generated by a set  is the group freely generated by . Every group generated by  is isomorphic to a quotient of this group, a feature which is utilized in the expression of a group's presentation.
  Frattini subgroup
  An interesting companion topic is that of non-generators. An element  of the group  is a non-generator if every set  containing  that generates , still generates  when  is removed from . In the integers with addition, the only non-generator is 0. The set of all non-generators forms a subgroup of , the Frattini subgroup.