 Finitely generated group

A group is finitely generated when it has a finite generating set of a group.

A finitely generated group is a group \( G \) that can be generated by a finite set of elements. More formally, there exists a finite set of elements \( \{ g_1, g_2, \ldots, g_n \} \) in \( G \) such that every element \( g \in G \) can be expressed as a finite combination of these generators and their inverses.