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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

General trinomials having symmetric Galois group
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by John Howard Smith
Proc. Amer. Math. Soc. 63 (1977), 208-212
DOI: https://doi.org/10.1090/S0002-9939-1977-0437508-6

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), 670โ€“678. 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
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Bibliographic 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