Polynomials with Frobenius groups of prime degree as Galois groups II

Abstract We present characterization theorems for polynomials of prime degree p ≥ 5 over Q with Frobenius groups of degree p: Fpl = Flp′, l| p − 1 as Galois groups. We construct a generic family of polynomials with Galois group F p(p − 1) 2 (p ≡ 3 (mod 4)), using the pth Chebyshev polynomial of the first kind. In addition, a parametric family of quintic polynomials with Galois group F20 is given. Explicit examples of polynomials are presented for F2p = Dp (p ≤ 19), F20 and for F p(p − 1) 2 with p = 7 and 11. Some properties of Frobenius fields are also discussed.

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