Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 31, No. 2, pp. 207-214 (2015)

Polynomials with a given cyclic Galois group

Jiri Cihlar, Jaroslav Fuka and Martin Kuril

J.E. Purkyne University

Abstract: For every natural number $n$ such that $2n+1$ is a prime, we present an explicit monic irreducible $n$th degree polynomial with integer coefficients whose Galois group over the field of all rational numbers is isomorphic to the cyclic group $Z_n$. The discriminant of the splitting field of the presented polynomial is equal to $(2n+1)^{n-1}$.

Keywords: Galois group of a polynomial, discriminant of a number field.

Classification (MSC2000): 12F12; 11R20

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number]
© 2015 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition