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- Composition_series abstract "In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that many naturally occurring modules are not semisimple, hence cannot be decomposed into a direct sum of simple modules. A composition series of a module M is a finite increasing filtration of M by submodules such that the successive quotients are simple and serves as a replacement of the direct sum decomposition of M into its simple constituents. A composition series may not exist, and when it does, it need not be unique. Nevertheless, a group of results known under the general name Jordan–Hölder theorem asserts that whenever composition series exist, the isomorphism classes of simple pieces (although, perhaps, not their location in the composition series in question) and their multiplicities are uniquely determined. Composition series may thus be used to define invariants of finite groups and Artinian modules.A related but distinct concept is a chief series: a composition series is a maximal subnormal series, while a chief series is a maximal normal series.".
- Composition_series wikiPageExternalLink 1183497873.
- Composition_series wikiPageID "297493".
- Composition_series wikiPageLength "8714".
- Composition_series wikiPageOutDegree "49".
- Composition_series wikiPageRevisionID "661348964".
- Composition_series wikiPageWikiLink Abelian_category.
- Composition_series wikiPageWikiLink Abstract_algebra.
- Composition_series wikiPageWikiLink Artinian_module.
- Composition_series wikiPageWikiLink Artinian_ring.
- Composition_series wikiPageWikiLink Bulletin_of_the_American_Mathematical_Society.
- Composition_series wikiPageWikiLink Camille_Jordan.
- Composition_series wikiPageWikiLink Category:Module_theory.
- Composition_series wikiPageWikiLink Category:Subgroup_series.
- Composition_series wikiPageWikiLink Category_(mathematics).
- Composition_series wikiPageWikiLink Chief_series.
- Composition_series wikiPageWikiLink Direct_sum_of_modules.
- Composition_series wikiPageWikiLink Filtration_(abstract_algebra).
- Composition_series wikiPageWikiLink Filtration_(mathematics).
- Composition_series wikiPageWikiLink Finite_group.
- Composition_series wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Composition_series wikiPageWikiLink Glossary_of_category_theory.
- Composition_series wikiPageWikiLink Group_(mathematics).
- Composition_series wikiPageWikiLink Group_with_operators.
- Composition_series wikiPageWikiLink If_and_only_if.
- Composition_series wikiPageWikiLink Infinite_group.
- Composition_series wikiPageWikiLink Inner_automorphism.
- Composition_series wikiPageWikiLink Isomorphism.
- Composition_series wikiPageWikiLink Isomorphism_class.
- Composition_series wikiPageWikiLink Krohn–Rhodes_theory.
- Composition_series wikiPageWikiLink Length_of_an_object.
- Composition_series wikiPageWikiLink Maximal_element.
- Composition_series wikiPageWikiLink Module_(mathematics).
- Composition_series wikiPageWikiLink Noetherian_module.
- Composition_series wikiPageWikiLink Normal_series.
- Composition_series wikiPageWikiLink Normal_subgroup.
- Composition_series wikiPageWikiLink Object_(category_theory).
- Composition_series wikiPageWikiLink Otto_Hölder.
- Composition_series wikiPageWikiLink Permutation.
- Composition_series wikiPageWikiLink Quotient_object.
- Composition_series wikiPageWikiLink Schreier_refinement_theorem.
- Composition_series wikiPageWikiLink Semisimple_module.
- Composition_series wikiPageWikiLink Simple_group.
- Composition_series wikiPageWikiLink Simple_module.
- Composition_series wikiPageWikiLink Simple_object.
- Composition_series wikiPageWikiLink Subgroup_series.
- Composition_series wikiPageWikiLink Submodule.
- Composition_series wikiPageWikiLink Subnormal_series.
- Composition_series wikiPageWikiLink Subobject.
- Composition_series wikiPageWikiLink Transfinite_induction.
- Composition_series wikiPageWikiLink Up_to.
- Composition_series wikiPageWikiLink Zassenhaus_lemma.
- Composition_series wikiPageWikiLinkText "Composition series".
- Composition_series wikiPageWikiLinkText "Composition series#Uniqueness: Jordan–Hölder theorem".
- Composition_series wikiPageWikiLinkText "Jordan–Hölder theorem on composition series".
- Composition_series wikiPageWikiLinkText "composition factors".
- Composition_series wikiPageWikiLinkText "composition length".
- Composition_series wikiPageWikiLinkText "composition series".
- Composition_series hasPhotoCollection Composition_series.
- Composition_series wikiPageUsesTemplate Template:Citation.
- Composition_series wikiPageUsesTemplate Template:Harv.
- Composition_series wikiPageUsesTemplate Template:Refimprove.
- Composition_series wikiPageUsesTemplate Template:Reflist.
- Composition_series wikiPageUsesTemplate Template:See_also.
- Composition_series wikiPageUsesTemplate Template:Sfn.
- Composition_series subject Category:Module_theory.
- Composition_series subject Category:Subgroup_series.
- Composition_series type Article.
- Composition_series type Article.
- Composition_series type Thing.
- Composition_series comment "In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that many naturally occurring modules are not semisimple, hence cannot be decomposed into a direct sum of simple modules.".
- Composition_series label "Composition series".
- Composition_series seeAlso Length_of_a_module.
- Composition_series sameAs סדרה_נורמלית.
- Composition_series sameAs Serie_di_composizione.
- Composition_series sameAs 組成列.
- Composition_series sameAs Ciąg_kompozycyjny.
- Composition_series sameAs m.01rgg9.
- Composition_series sameAs Q2525646.
- Composition_series sameAs Q2525646.
- Composition_series sameAs 合成列.
- Composition_series wasDerivedFrom Composition_series?oldid=661348964.
- Composition_series isPrimaryTopicOf Composition_series.