Vol. 90, No. 1, 1980

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The Galois group of a polynomial with two indeterminate coefficients

Stephen D. Cohen

Vol. 90 (1980), No. 1, 63–76
Abstract

Suppose that f(x) = i=0nαiXi(α0αn0) is a polynomial in which two of the coefficients are indeterminates t, u and the remainder belong to a field F. We find the galois group of f over F(t,u). In particular, it is the full symmetric group Sn provided that (as is obviously necessary) f(X)f1(Xr) for any r > 1. The results are always valid if F has characteristic zero and hold under mild conditions involving the characteristic of F otherwise. Work of Uchida [10] and Smith [9] is extended even in the case of trinomials Xn + tXa + u on which they concentrated.

Mathematical Subject Classification 2000
Primary: 12E05
Secondary: 12F10
Milestones
Received: 9 May 1979
Published: 1 September 1980
Authors
Stephen D. Cohen
University of Glasgow
Glasgow
United Kingdom