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- Finitely_generated_abelian_group abstract "In abstract algebra, an abelian group (G, +) is called finitely generated if there exist finitely many elements x1, ..., xs in G such that every x in G can be written in the formx = n1x1 + n2x2 + ... + nsxswith integers n1, ..., ns. In this case, we say that the set {x1, ..., xs} is a generating set of G or that x1, ..., xs generate G.Clearly, every finite abelian group is finitely generated. The finitely generated abelian groups are of a rather simple structure and can be completely classified, as will be explained below.".
- Finitely_generated_abelian_group wikiPageID "58527".
- Finitely_generated_abelian_group wikiPageLength "6508".
- Finitely_generated_abelian_group wikiPageOutDegree "42".
- Finitely_generated_abelian_group wikiPageRevisionID "675926676".
- Finitely_generated_abelian_group wikiPageWikiLink Abelian_category.
- Finitely_generated_abelian_group wikiPageWikiLink Abelian_group.
- Finitely_generated_abelian_group wikiPageWikiLink Abstract_algebra.
- Finitely_generated_abelian_group wikiPageWikiLink Category:Abelian_group_theory.
- Finitely_generated_abelian_group wikiPageWikiLink Category:Algebraic_structures.
- Finitely_generated_abelian_group wikiPageWikiLink Category:Fundamental_theorems.
- Finitely_generated_abelian_group wikiPageWikiLink Category_of_abelian_groups.
- Finitely_generated_abelian_group wikiPageWikiLink Chinese_remainder_theorem.
- Finitely_generated_abelian_group wikiPageWikiLink Composition_series.
- Finitely_generated_abelian_group wikiPageWikiLink Coprime.
- Finitely_generated_abelian_group wikiPageWikiLink Coprime_integers.
- Finitely_generated_abelian_group wikiPageWikiLink Corollary.
- Finitely_generated_abelian_group wikiPageWikiLink Cyclic_group.
- Finitely_generated_abelian_group wikiPageWikiLink Direct_sum_of_groups.
- Finitely_generated_abelian_group wikiPageWikiLink Divisor.
- Finitely_generated_abelian_group wikiPageWikiLink Factor_group.
- Finitely_generated_abelian_group wikiPageWikiLink Free_abelian_group.
- Finitely_generated_abelian_group wikiPageWikiLink Generating_set_of_a_group.
- Finitely_generated_abelian_group wikiPageWikiLink Group_homomorphism.
- Finitely_generated_abelian_group wikiPageWikiLink Infinite_set.
- Finitely_generated_abelian_group wikiPageWikiLink Integer.
- Finitely_generated_abelian_group wikiPageWikiLink Integers.
- Finitely_generated_abelian_group wikiPageWikiLink Invariant_factor.
- Finitely_generated_abelian_group wikiPageWikiLink Jordan–Hölder_theorem.
- Finitely_generated_abelian_group wikiPageWikiLink Lattice_(group).
- Finitely_generated_abelian_group wikiPageWikiLink Modular_arithmetic.
- Finitely_generated_abelian_group wikiPageWikiLink Natural_number.
- Finitely_generated_abelian_group wikiPageWikiLink Order_(group_theory).
- Finitely_generated_abelian_group wikiPageWikiLink Order_of_a_group.
- Finitely_generated_abelian_group wikiPageWikiLink Primary_cyclic_group.
- Finitely_generated_abelian_group wikiPageWikiLink Prime_number.
- Finitely_generated_abelian_group wikiPageWikiLink Principal_ideal_domain.
- Finitely_generated_abelian_group wikiPageWikiLink Quotient_group.
- Finitely_generated_abelian_group wikiPageWikiLink Rank_of_an_abelian_group.
- Finitely_generated_abelian_group wikiPageWikiLink Rational_number.
- Finitely_generated_abelian_group wikiPageWikiLink Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain.
- Finitely_generated_abelian_group wikiPageWikiLink Subcategory.
- Finitely_generated_abelian_group wikiPageWikiLink Subgroup.
- Finitely_generated_abelian_group wikiPageWikiLink Torsion-free_abelian_group.
- Finitely_generated_abelian_group wikiPageWikiLink Torsion_subgroup.
- Finitely_generated_abelian_group wikiPageWikiLink Undergraduate_Texts_in_Mathematics.
- Finitely_generated_abelian_group wikiPageWikiLink Up_to.
- Finitely_generated_abelian_group wikiPageWikiLinkText "Finitely generated abelian group".
- Finitely_generated_abelian_group wikiPageWikiLinkText "Finitely generated abelian group#Classification".
- Finitely_generated_abelian_group wikiPageWikiLinkText "classification of finitely generated abelian groups".
- Finitely_generated_abelian_group wikiPageWikiLinkText "finitely generated abelian group".
- Finitely_generated_abelian_group wikiPageWikiLinkText "finitely generated groups".
- Finitely_generated_abelian_group wikiPageWikiLinkText "finitely generated".
- Finitely_generated_abelian_group hasPhotoCollection Finitely_generated_abelian_group.
- Finitely_generated_abelian_group wikiPageUsesTemplate Template:Cite_book.
- Finitely_generated_abelian_group wikiPageUsesTemplate Template:Fundamental_theorems.
- Finitely_generated_abelian_group wikiPageUsesTemplate Template:Null.
- Finitely_generated_abelian_group wikiPageUsesTemplate Template:Reflist.
- Finitely_generated_abelian_group subject Category:Abelian_group_theory.
- Finitely_generated_abelian_group subject Category:Algebraic_structures.
- Finitely_generated_abelian_group subject Category:Fundamental_theorems.
- Finitely_generated_abelian_group comment "In abstract algebra, an abelian group (G, +) is called finitely generated if there exist finitely many elements x1, ..., xs in G such that every x in G can be written in the formx = n1x1 + n2x2 + ... + nsxswith integers n1, ..., ns. In this case, we say that the set {x1, ..., xs} is a generating set of G or that x1, ..., xs generate G.Clearly, every finite abelian group is finitely generated.".
- Finitely_generated_abelian_group label "Finitely generated abelian group".
- Finitely_generated_abelian_group sameAs Endlich_erzeugte_abelsche_Gruppe.
- Finitely_generated_abelian_group sameAs Lõplikult_moodustatud_Abeli_rühm.
- Finitely_generated_abelian_group sameAs Groupe_abélien_de_type_fini.
- Finitely_generated_abelian_group sameAs חבורה_אבלית_נוצרת_סופית.
- Finitely_generated_abelian_group sameAs 有限生成アーベル群.
- Finitely_generated_abelian_group sameAs 유한생성_아벨_군.
- Finitely_generated_abelian_group sameAs Skończenie_generowana_grupa_przemienna.
- Finitely_generated_abelian_group sameAs m.0f_kd.
- Finitely_generated_abelian_group sameAs Конечнопорождённая_абелева_группа.
- Finitely_generated_abelian_group sameAs Скінченнопороджена_абелева_група.
- Finitely_generated_abelian_group sameAs Q142140.
- Finitely_generated_abelian_group sameAs Q142140.
- Finitely_generated_abelian_group sameAs 有限生成阿貝爾群.
- Finitely_generated_abelian_group wasDerivedFrom Finitely_generated_abelian_group?oldid=675926676.
- Finitely_generated_abelian_group isPrimaryTopicOf Finitely_generated_abelian_group.