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The mathematical life of Cauchy’s group theorem. (English) Zbl 1065.01009
The first nontrivial result in permutation groups was the following theorem (stated but not proved by E. Galois, published 1846 by J. Liouville) of 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 H. Dedekind (1855–1858), G. Frobenius (1887), L. Sylow (1872), C. Jordan (1870) and G. A. Miller (1898) up to the most recent by J. H. MacKay (1959).
01A55Mathematics in the 19th century
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20-03Historical (group theory)