proof of Lagrange’s theorem

We know that the cosets Hg form a partitionMathworldPlanetmath of G (see the coset entry for proof of this.) Since G is finite, we know it can be completely decomposed into a finite number of cosets. Call this number n. We denote the ith coset by Hai and write G as


since each coset has |H| elements, we have


and so |H| divides |G|, which proves Lagrange’s theorem.

Title proof of Lagrange’s theorem
Canonical name ProofOfLagrangesTheorem
Date of creation 2013-03-22 12:15:47
Last modified on 2013-03-22 12:15:47
Owner akrowne (2)
Last modified by akrowne (2)
Numerical id 6
Author akrowne (2)
Entry type Proof
Classification msc 20D99