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- Cauchy's_theorem_(group_theory) abstract "Cauchy's theorem is a theorem in the mathematics of group theory, named after Augustin Louis Cauchy. It states that if G is a finite group and p is a prime number dividing the order of G (the number of elements in G), then G contains an element of order p. That is, there is x in G so that p is the lowest non-zero number with xp = e, where e is the identity element.The theorem is related to Lagrange's theorem, which states that the order of any subgroup of a finite group G divides the order of G. Cauchy's theorem implies that for any prime divisor p of the order of G, there is a subgroup of G whose order is p—the cyclic group generated by the element in Cauchy's theorem.Cauchy's theorem is generalised by Sylow's first theorem, which implies that if pn is any prime power dividing the order of G, then G has a subgroup of order pn.".
- Cauchy's_theorem_(group_theory) wikiPageID "2838129".
- Cauchy's_theorem_(group_theory) wikiPageRevisionID "594386199".
- Cauchy's_theorem_(group_theory) hasPhotoCollection Cauchy's_theorem_(group_theory).
- Cauchy's_theorem_(group_theory) id "1569".
- Cauchy's_theorem_(group_theory) id "2186".
- Cauchy's_theorem_(group_theory) title "Cauchy's theorem".
- Cauchy's_theorem_(group_theory) title "Proof of Cauchy's theorem".
- Cauchy's_theorem_(group_theory) subject Category:Articles_containing_proofs.
- Cauchy's_theorem_(group_theory) subject Category:Finite_groups.
- Cauchy's_theorem_(group_theory) subject Category:Theorems_in_group_theory.
- Cauchy's_theorem_(group_theory) type Abstraction100002137.
- Cauchy's_theorem_(group_theory) type Communication100033020.
- Cauchy's_theorem_(group_theory) type FiniteGroups.
- Cauchy's_theorem_(group_theory) type Group100031264.
- Cauchy's_theorem_(group_theory) type Message106598915.
- Cauchy's_theorem_(group_theory) type Proposition106750804.
- Cauchy's_theorem_(group_theory) type Statement106722453.
- Cauchy's_theorem_(group_theory) type Theorem106752293.
- Cauchy's_theorem_(group_theory) type TheoremsInGroupTheory.
- Cauchy's_theorem_(group_theory) comment "Cauchy's theorem is a theorem in the mathematics of group theory, named after Augustin Louis Cauchy. It states that if G is a finite group and p is a prime number dividing the order of G (the number of elements in G), then G contains an element of order p.".
- Cauchy's_theorem_(group_theory) label "Cauchy's theorem (group theory)".
- Cauchy's_theorem_(group_theory) label "Satz von Cauchy (Gruppentheorie)".
- Cauchy's_theorem_(group_theory) label "Stelling van Cauchy".
- Cauchy's_theorem_(group_theory) label "Teorema de Cauchy (teoría de grupos)".
- Cauchy's_theorem_(group_theory) label "Teorema di Cauchy (teoria dei gruppi)".
- Cauchy's_theorem_(group_theory) label "Théorème de Cauchy (groupes)".
- Cauchy's_theorem_(group_theory) label "Twierdzenie Cauchy'ego (teoria grup)".
- Cauchy's_theorem_(group_theory) label "Теорема Коши (теория групп)".
- Cauchy's_theorem_(group_theory) label "مبرهنة كوشي (نظرية الزمر)".
- Cauchy's_theorem_(group_theory) label "コーシーの定理 (群論)".
- Cauchy's_theorem_(group_theory) label "柯西定理 (群論)".
- Cauchy's_theorem_(group_theory) sameAs Satz_von_Cauchy_(Gruppentheorie).
- Cauchy's_theorem_(group_theory) sameAs Teorema_de_Cauchy_(teoría_de_grupos).
- Cauchy's_theorem_(group_theory) sameAs Théorème_de_Cauchy_(groupes).
- Cauchy's_theorem_(group_theory) sameAs Teorema_di_Cauchy_(teoria_dei_gruppi).
- Cauchy's_theorem_(group_theory) sameAs コーシーの定理_(群論).
- Cauchy's_theorem_(group_theory) sameAs 코시의_정리_(군론).
- Cauchy's_theorem_(group_theory) sameAs Stelling_van_Cauchy.
- Cauchy's_theorem_(group_theory) sameAs Twierdzenie_Cauchy'ego_(teoria_grup).
- Cauchy's_theorem_(group_theory) sameAs m.085yzh.
- Cauchy's_theorem_(group_theory) sameAs Q1139041.
- Cauchy's_theorem_(group_theory) sameAs Q1139041.
- Cauchy's_theorem_(group_theory) sameAs Cauchy's_theorem_(group_theory).
- Cauchy's_theorem_(group_theory) wasDerivedFrom Cauchy's_theorem_(group_theory)?oldid=594386199.
- Cauchy's_theorem_(group_theory) isPrimaryTopicOf Cauchy's_theorem_(group_theory).