Editing Finitely generated group (section)

== Examples ==
* Every [[quotient group|quotient]] of a finitely generated group ''G'' is finitely generated; the quotient group is generated by the images of the generators of ''G'' under the [[Quotient group#Properties|canonical projection]].
* A group that is generated by a single element is called [[cyclic group|cyclic]]. Every infinite cyclic group is [[group isomorphism|isomorphic]] to the additive group of the [[Integer#Algebraic properties|integers]] '''Z'''.
** A [[locally cyclic group]] is a group in which every finitely generated [[subgroup]] is cyclic.
* The [[free group]] on a finite set is finitely generated by the elements of that set ([[Generating set of a group#Examples|§Examples]]).
* [[Argumentum a fortiori|A fortiori]], every [[Presentation of a group#Definition|finitely presented group]] ([[Presentation of a group#Examples|§Examples]]) is finitely generated.