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Integer polynomials with roots mod $$p$$ for all primes $$p$$. (English) Zbl 1052.12002
Summary: Let $$f(X)$$ be an integer polynomial which is a product of two irreducible factors. Assume that $$f(X)$$ has a root mod $$p$$ for all primes $$p$$. If the splitting field of $$f(X)$$ over the rationals is a cyclic extension of the stem fields, then the Galois group of $$f(X)$$ over the rationals is soluble and of bounded Fitting length. Moreover, the fixed groups of the stem extensions are in, some sense, unique.

##### MSC:
 12F10 Separable extensions, Galois theory 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, $$\pi$$-length, ranks
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