Tokyo Journal of Mathematics

A Note on the Construction of Metacyclic Extensions

Shin NAKANO and Masahiko SASE

Full-text: Open access


Let $p$ be an odd prime and $r$ a divisor of $p-1$. We present a characterization of metacyclic extensions of degree $pr$ containing a given cyclic extension of degree $r$ over a field of characteristic other than $p$. Furthermore, we give a method of constructing polynomials with Galois groups which are Frobenius groups of degree $p$.

Article information

Tokyo J. Math., Volume 25, Number 1 (2002), 197-203.

First available in Project Euclid: 5 June 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


NAKANO, Shin; SASE, Masahiko. A Note on the Construction of Metacyclic Extensions. Tokyo J. Math. 25 (2002), no. 1, 197--203. doi:10.3836/tjm/1244208946.

Export citation


  • A. A. Bruen, C. U. Jensen and N. Yui, Polynomials with Frobenius groups of prime degree as Galois groups num2, J. Number Theory, 24 (1986), 305–359.
  • H. Cohen, Advanced topics in computational number theory, Springer (2000).
  • B. Huppert, Endliche Gruppen num1, Springer (1967).
  • M. Imaoka and Y. Kishi, Spiegelung relation between dihedral extensions and Frobenius extensions, preprint.