✦ LIBER ✦
Integer Polynomials with Roots mod p for all Primes p
✍ Scribed by Rolf Brandl
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 128 KB
- Volume
- 240
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
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.