About: Lagrange's theorem (group theory)

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In the mathematical field of group theory, Lagrange's theorem is a theorem that states that for any finite group G, the order (number of elements) of every subgroup of G divides the order of G. The theorem is named after Joseph-Louis Lagrange. The following variant states that for a subgroup of a finite group , not only is an integer, but also that its value is the index , defined as the number of left cosets of in . Lagrange's theorem — If H is a subgroup of a group G, then This variant holds even if is infinite, provided that , , and are interpreted as cardinal numbers.

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rdf:type	Thing
rdfs:label	Lagrange's theorem (group theory) (en)
rdfs:comment	In the mathematical field of group theory, Lagrange's theorem is a theorem that states that for any finite group G, the order (number of elements) of every subgroup of G divides the order of G. The theorem is named after Joseph-Louis Lagrange. The following variant states that for a subgroup of a finite group , not only is an integer, but also that its value is the index , defined as the number of left cosets of in . Lagrange's theorem — If H is a subgroup of a group G, then This variant holds even if is infinite, provided that , , and are interpreted as cardinal numbers. (en)
sameAs	Lagrange's theorem (group theory) Lagrange's theorem (group theory)
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Subject	Articles containing proofs Theorems about finite groups
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Lagrange's_theorem_(group_theory)?oldid=1067064649&ns=0
Wikipage page ID	31150 (xsd:integer)
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Wikipage revision ID	1067064649 (xsd:integer)
Link from a Wikipage to another Wikipage	Supersolvable group Unitary divisor Wiley (publisher) Alternating group Augustin-Louis Cauchy Camille Jordan Cardinal number Carl Friedrich Gauss Articles containing proofs Cauchy's theorem (group theory) Generating set of a group Joseph-Louis Lagrange Disjoint sets Disquisitiones Arithmeticae Divisor Mersenne prime Q.E.D. Cyclic group Prime number Coset Order (group theory) Partition of a set Solvable group Equivalence class Equivalence relation Finite group Identity element Index of a subgroup Permutation group Sylow theorems Symmetric group Fermat's little theorem Group theory Hall subgroup Modular arithmetic Euler's theorem Subgroup Klein four-group Mathematics Mathematics Magazine Multiplicative group Simple group Wilson's theorem Theorems about finite groups
has abstract	In the mathematical field of group theory, Lagrange's theorem is a theorem that states that for any finite group G, the order (number of elements) of every subgroup of G divides the order of G. The theorem is named after Joseph-Louis Lagrange. The following variant states that for a subgroup of a finite group , not only is an integer, but also that its value is the index , defined as the number of left cosets of in . Lagrange's theorem — If H is a subgroup of a group G, then This variant holds even if is infinite, provided that , , and are interpreted as cardinal numbers. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Lagrange's_theorem_(group_theory)
is Wikipage redirect of	Lagrange's Group Theorem Lagrange's group theorem Lagrange theorem (group theory)
is Link from a Wikipage to another Wikipage of	Group (mathematics) List of theorems List of things named after Joseph-Louis Lagrange Alternating group Burnside's lemma Cauchy's theorem (group theory) Joseph-Louis Lagrange Dihedral group of order 6 Dirichlet character Double coset Lenstra elliptic-curve factorization Cyclic group Degree of a field extension Hopf algebra List of Italian inventions and discoveries List of group theory topics List of mathematical jargon List of mathematical proofs List of scientific laws named after people Closure with a twist Coset Counting points on elliptic curves ElGamal encryption Cubic function

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