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Galois and the simple group of order 60
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Stewart, Ian (2024) Galois and the simple group of order 60. Archive for History of Exact Sciences, 78 . pp. 1-28. doi:10.1007/s00407-023-00319-9 ISSN 0003-9519. (In Press)
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Official URL: https://doi.org/10.1007/s00407-023-00319-9
Abstract
In his testamentary letter to Auguste Chevalier, Évariste Galois states that, in modern terminology, the smallest simple group has order 60. No proof of this statement survives in his papers, and it has been suggested that a proof would have been impossible using the methods available at the time. We argue that this assertion is unduly pessimistic. Moreover, one fragmentary document, dismissed as a triviality and misunderstood, looks suspiciously like cryptic notes related to this result. We give an elementary proof of Galois’s statement, explain why it is likely that he would have been aware of the methods involved, and discuss the potential relevance of the fragment.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Group theory, Galois, Évariste, 1811-1832 | ||||||||
Journal or Publication Title: | Archive for History of Exact Sciences | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0003-9519 | ||||||||
Official Date: | January 2024 | ||||||||
Dates: |
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Volume: | 78 | ||||||||
Page Range: | pp. 1-28 | ||||||||
DOI: | 10.1007/s00407-023-00319-9 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | In Press | ||||||||
Re-use Statement: | This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00407-023-00319-9 | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 21 November 2023 |
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