proof of Lagrange’s theorem
We know that the cosets form a partition of (see the coset entry for proof of this.) Since is finite, we know it can be completely decomposed into a finite number of cosets. Call this number . We denote the th coset by and write as
since each coset has elements, we have
and so divides , which proves Lagrange’s theorem.
|Title||proof of Lagrange’s theorem|
|Date of creation||2013-03-22 12:15:47|
|Last modified on||2013-03-22 12:15:47|
|Last modified by||akrowne (2)|