of abstract groups, this result of Lagrange on polynomials was recognized to extend to the general theorem about finite groups which now bears his name. In his Disquisitiones Arithmeticae in 1801, Carl Friedrich Gauss proved Lagrange's theorem for the special case of , the multiplicative group of nonzero integers modulo , where is a prime. In 1844, Augustin-Louis Cauchy proved Lagrange's theorem for the symmetric group . Camille Jordan finally proved Lagrange's theorem for the case of any permutation group in 1861. Notes References External links Theorems about finite groups Articles containing proofs