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Proceedings of the American Mathematical Society

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General trinomials having symmetric Galois group


Author: John Howard Smith
Journal: Proc. Amer. Math. Soc. 63 (1977), 208-212
MSC: Primary 12E05
Erratum: Proc. Amer. Math. Soc. 77 (1979), 298.
MathSciNet review: 0437508
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Abstract: Let a and b be independent transcendentals over a field F and let $ n > k$ be integers $ > 1$ with $ n,k,n - k$ and the characteristic of F pairwise relatively prime. Then the Galois group of $ {x^n} + a{x^k} + b$ over $ F(a,b)$ is $ {S_n}$.


References [Enhancements On Off] (What's this?)

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  • [2] Kôji Uchida, Galois group of an equation 𝑋ⁿ-𝑎𝑋+𝑏=0, Tôhoku Math. J. (2) 22 (1970), 670–678. MR 0277505
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  • [4] Helmut Wielandt, Finite permutation groups, Translated from the German by R. Bercov, Academic Press, New York-London, 1964. MR 0183775

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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0437508-6
Article copyright: © Copyright 1977 American Mathematical Society