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fundamental theorem of finitely generated abelian groups

Theorem 1 (Fundamental Theorem of Finitely Generated Abelian Groups)

Let $G$ be a finitely generated abelian group. Then there is a unique expression of the form: $$G\cong \Ints^{r}\oplus\Ints/n_1\Ints\oplus\Ints/n_2\Ints\oplus\ldots\oplus\Ints/n_s\Ints$$ for some integers $r,n_i$ satisfying: $$r\geq 0;\quad \forall i, n_i\geq 2;\quad n_{i+1}\mid n_i\ \text{for } 1\leq i\leq s-1.$$

fundamental theorem of finitely generated abelian groups is owned by alozano, Pedro Sanchez.

How to Cite This Entry

alozano, Pedro Sanchez. "fundamental theorem of finitely generated abelian groups" (version 3). PlanetMath.org. Freely available at http://planetmath.org/FundamentalTheoremOfFinitelyGeneratedAbelianGroups.html.

Classification

AMS MSC:

20E34 (Group theory and generalizations :: Structure and classification of infinite or finite groups :: General structure theorems)

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