General trinomials having symmetric Galois group
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- by John Howard Smith PDF
- Proc. Amer. Math. Soc. 63 (1977), 208-212 Request permission
Erratum: Proc. Amer. Math. Soc. 77 (1979), 298.
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
- Nicolas Bourbaki, Elements of mathematics. Commutative algebra, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass., 1972. Translated from the French. MR 0360549
- Kรดji Uchida, Galois group of an equation $X^{n}-aX+b=0$, Tohoku Math. J. (2) 22 (1970), 670โ678. MR 277505, DOI 10.2748/tmj/1178242731 B. L. van der Waerden, Modern algebra, Vol. 1, Springer-Verlag, Berlin, 1937; rev. English transl., Ungar, New York, 1953. MR 2, 120; 10, 587.
- Helmut Wielandt, Finite permutation groups, Academic Press, New York-London, 1964. Translated from the German by R. Bercov. MR 0183775
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 208-212
- MSC: Primary 12E05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0437508-6
- MathSciNet review: 0437508