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finitely generated abelian group classification of finitely generated abelian groups finitely-generated abelian group finitely generated abelian groups fundamental theorem of finitely generated abelian groups
EN
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}}.
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