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fundamental theorem of finitely generated abelian groups

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Theorem 1 (Fundamental Theorem of Finitely Generated Abelian Groups)

Let be a finitely generated abelian group. Then there is a unique expression of the form:

$\displaystyle G\cong \mathbb{Z}^{r}\oplus\mathbb{Z}/n_1\mathbb{Z}\oplus\mathbb{Z}/n_2\mathbb{Z}\oplus\ldots\oplus\mathbb{Z}/n_s\mathbb{Z}$

for some integers satisfying:

$\displaystyle r\geq 0;\quad \forall i, n_i\geq 2;\quad n_{i+1}\mid n_i\$ for $\displaystyle 1\leq i\leq s-1.$

"fundamental theorem of finitely generated abelian groups" is owned by alozano. [ full author list (2) | owner history (1) ]

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fundamental theorem of finitely generated abelian groups

Keywords:

finitely generated, abelian group

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Cross-references: integers, expression, abelian groups, finitely generated
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This is version 2 of fundamental theorem of finitely generated abelian groups, born on 2003-08-25, modified 2004-03-17.
Object id is 4652, canonical name is FundamentalTheoremOfFinitelyGeneratedAbelianGroups.
Accessed 7355 times total.

Classification:

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

Pending Errata and Addenda

1. synonym by asteroid on 2008-05-03 19:45:57
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