Galois groups of trinomials

[摘要] Galois groups of irreducible trinomials X-n + aX(s) + b is an element of Z[X] are investigated assuming the classification of finite simple groups. We show that under some simple yet general hypotheses bearing on the integers n, s, a and b only very specific groups can occur. For instance, if the two integers nb and as(n - s) are coprime and if s is a prime number, then already the Galois group of f(X) is either the alternating group A(n) or the symmetric group S-n. This significantly extends work of Osada. (C) 1999 Academic Press.

[发布日期] 1999-12-15