The mathematical life of Cauchy's group theorem
type: Item
instance of: scholarly article
title: The mathematical life of Cauchy's group theorem
zbMATH Open document ID: 1065.01009
DOI: 10.1016/S0315-0860(03)00003-X
author: Yanyan Li
published in: Historia Mathematica
publication date: 2004-08-19T00:00:00Z
review text: 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).
reviewed by: Roman Duda
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 20-03
zbMATH DE Number: 2092859
zbMATH Keywords: Cauchy's theorem
zbMATH Keywords: Permutation groups
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: History of finite
zbMATH Keywords: group theory
MaRDI profile type: Publication
Wikidata QID: Q56092194
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description: scientific article; zbMATH DE number 2092859