KnowraJordan–Hölder theoremLinked fromLinked fromThe 9 pages that link to Jordan–Hölder theorem, each with the reason it gives.All 9Broader topic 1Related 6Compared with 2Alternating groupRelated: Alternating groups appear as composition factors in the structure theory of finite groups.Simple groupRelated: It makes the simple factors intrinsic to a finite group.Camille JordanBroader topic: The theorem bears Jordan’s name and captures a central result of his group-theoretic work.Composition seriesRelated: It guarantees that different composition series yield the same factors, counted with multiplicity.Finite simple groupRelated: It makes the simple factors intrinsic to the finite group being analyzed.Classification of finite simple groupsRelated: The classification identifies the possible simple factors in finite groups.Isomorphism theoremsCompared with: It classifies composition factors, while the isomorphism theorems relate particular quotients and subgroups.Wedderburn–Artin theoremCompared with: It concerns uniqueness of simple factors, rather than identifying rings as matrix products.Zassenhaus lemmaRelated: The refinement argument uses the lemma to compare factors from different composition series.