The mathematical life of Cauchy's group theorem

Abstract

Cauchy's theorem on the order of finite groups is a fixture of elementary course work in abstract algebra today: its proof is a straightforward exercise in the application of general mathematical tools. The initial proof by Cauchy, however, was unprecedented in its complex computations involving permutational group theory and contained an egregious error. A direct inspiration to Sylow's theorem, Cauchy's theorem was reworked by R. Dedekind, G.F. Frobenius, C. Jordan, and J.H. McKay in ever more natural, concise terms. Its most succinct form employs just the structure lacking in Cauchy's original proof—the wreath product.