The mathematical life of Cauchy's group theorem (Q1877690)

The first nontrivial result in permutation groups was the following theorem (stated but not proved by \textit{E. Galois}, published 1846 by \textit{J. Liouville}) of \textit{Cauchy} (1844): Every group whose order is divisible by a prime number \(p\) has a subgroup of order \(p\). The paper tells the story of that theorem. It starts with a detailed analysis of the (uncomplete) proof by Cauchy and proceeds through its reworkings by \textit{H. Dedekind} (1855--1858), \textit{G. Frobenius} (1887), \textit{L. Sylow} (1872), \textit{C. Jordan} (1870) and \textit{G. A. Miller} (1898) up to the most recent by \textit{J. H. MacKay} (1959).