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Zbl 1065.01009
Meo, M.
The mathematical life of Cauchy's group theorem. (English)
[J] Hist. Math. 31, No. 2, 196-221 (2004). ISSN 0315-0860

The first nontrivial result in permutation groups was the following theorem (stated but not proved by {\it E. Galois}, published 1846 by {\it J. Liouville}) of {\it 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 {\it H. Dedekind} (1855--1858), {\it G. Frobenius} (1887), {\it L. Sylow} (1872), {\it C. Jordan} (1870) and {\it G. A. Miller} (1898) up to the most recent by {\it J. H. MacKay} (1959).
[Roman Duda (Wrocław)]

MSC 2000:: *01A55 Mathematics in the 19th century
01A60 Mathematics in the 20th century
20-03 Historical (group theory)

Keywords: Cauchy's theorem; Permutation groups; Sylow subgroups; History of finite; group theory

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