Finitely generated free group

Symbol-free definition
A group is said to be a finitely generated free group if it satisfies the following equivalent conditions:


 * It is finitely generated (that is, it has a finite generating set) and is also a free group
 * It is has a finite freely generating set, viz it is freely generated by a finite set

Definition with symbols
Often, people mean finitely generated free group when they just say free group.