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- Sylow_theorems abstract "In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Ludwig Sylow (1872) that give detailed information about the number of subgroups of fixed order that a given finite group contains. The Sylow theorems form a fundamental part of finite group theory and have very important applications in the classification of finite simple groups.For a prime number p, a Sylow p-subgroup (sometimes p-Sylow subgroup) of a group G is a maximal p-subgroup of G, i.e., a subgroup of G that is a p-group (so that the order of any group element is a power of p), and that is not a proper subgroup of any other p-subgroup of G. The set of all Sylow p-subgroups for a given prime p is sometimes written Sylp(G).The Sylow theorems assert a partial converse to Lagrange's theorem. While Lagrange's theorem states that for any finite group G the order (number of elements) of every subgroup of G divides the order of G, the Sylow theorems state that for any prime factor p of the order of a finite group G, there exists a Sylow p-subgroup of G. The order of a Sylow p-subgroup of a finite group G is pn, where n is the multiplicity of p in the order of G, and any subgroup of order pn is a Sylow p-subgroup of G. The Sylow p-subgroups of a group (for a given prime p) are conjugate to each other. The number of Sylow p-subgroups of a group for a given prime p is congruent to 1 mod p.".
- Sylow_theorems wikiPageExternalLink purl?GDZPPN002242052.
- Sylow_theorems wikiPageExternalLink sylow.pdf.
- Sylow_theorems wikiPageID "53993".
- Sylow_theorems wikiPageRevisionID "606253884".
- Sylow_theorems b "Abstract_Algebra/Group_Theory/The_Sylow_Theorems".
- Sylow_theorems commons "no".
- Sylow_theorems d "no".
- Sylow_theorems hasPhotoCollection Sylow_theorems.
- Sylow_theorems last "Kantor".
- Sylow_theorems n "no".
- Sylow_theorems q "no".
- Sylow_theorems s "no".
- Sylow_theorems species "no".
- Sylow_theorems v "no".
- Sylow_theorems voy "no".
- Sylow_theorems wikt "no".
- Sylow_theorems year "1985".
- Sylow_theorems year "1990".
- Sylow_theorems subject Category:Articles_containing_proofs.
- Sylow_theorems subject Category:Finite_groups.
- Sylow_theorems subject Category:P-groups.
- Sylow_theorems subject Category:Theorems_in_algebra.
- Sylow_theorems type Abstraction100002137.
- Sylow_theorems type Communication100033020.
- Sylow_theorems type FiniteGroups.
- Sylow_theorems type Group100031264.
- Sylow_theorems type Message106598915.
- Sylow_theorems type Proposition106750804.
- Sylow_theorems type Statement106722453.
- Sylow_theorems type Theorem106752293.
- Sylow_theorems type TheoremsInAlgebra.
- Sylow_theorems comment "In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Ludwig Sylow (1872) that give detailed information about the number of subgroups of fixed order that a given finite group contains.".
- Sylow_theorems label "Stellingen van Sylow".
- Sylow_theorems label "Sylow theorems".
- Sylow_theorems label "Sylow-Sätze".
- Sylow_theorems label "Teoremas de Sylow".
- Sylow_theorems label "Teoremi di Sylow".
- Sylow_theorems label "Théorèmes de Sylow".
- Sylow_theorems label "Twierdzenie Sylowa".
- Sylow_theorems label "Теоремы Силова".
- Sylow_theorems label "シローの定理".
- Sylow_theorems label "西羅定理".
- Sylow_theorems sameAs Sylowovy_věty.
- Sylow_theorems sameAs Sylow-Sätze.
- Sylow_theorems sameAs Teoremas_de_Sylow.
- Sylow_theorems sameAs Théorèmes_de_Sylow.
- Sylow_theorems sameAs Teoremi_di_Sylow.
- Sylow_theorems sameAs シローの定理.
- Sylow_theorems sameAs 실로우의_정리.
- Sylow_theorems sameAs Stellingen_van_Sylow.
- Sylow_theorems sameAs Twierdzenie_Sylowa.
- Sylow_theorems sameAs m.0f3t1.
- Sylow_theorems sameAs Q1057919.
- Sylow_theorems sameAs Q1057919.
- Sylow_theorems sameAs Sylow_theorems.
- Sylow_theorems wasDerivedFrom Sylow_theorems?oldid=606253884.
- Sylow_theorems isPrimaryTopicOf Sylow_theorems.