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≅ℤr⊕ℤ/n1ℤ⊕ℤ/n2ℤ⊕…⊕ℤ/nsℤ |
for some integers r,ni satisfying:
r≥0;∀i,ni≥2;ni+1∣nifor 1≤i≤s-1. |
Title | fundamental theorem of finitely generated abelian groups |
---|---|
Canonical name | FundamentalTheoremOfFinitelyGeneratedAbelianGroups |
Date of creation | 2013-03-22 13:54:12 |
Last modified on | 2013-03-22 13:54:12 |
Owner | alozano (2414) |
Last modified by | alozano (2414) |
Numerical id | 6 |
Author | alozano (2414) |
Entry type | Theorem |
Classification | msc 20E34 |
Synonym | classification of finitely generated abelian groups |
Related topic | AbelianGroupsOfOrder120 |
Related topic | FinitelyGenerated |
Related topic | AbelianGroup2 |
Defines | fundamental theorem of finitely generated abelian groups |