In abstract algebra, an abelian group is called finitely generated if there exist finitely many elements x 1, …, x s {\displaystyle x_{1},\dots,x_{s}} in G G such that every x x in G G can be written in the form x = n 1 x 1 + n 2 x 2 + ⋯ + n s x s {\displaystyle x=n_{1}x_{1}+n_{2}x_{2}+\cdots +n_{s}x_{s}} for some integers n 1, …, n s {\displaystyle n_{1},\dots,n_{s}}. Wikipedia