## Tokyo Journal of Mathematics

### A Note on the Construction of Metacyclic Extensions

#### Abstract

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

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

Dates
First available in Project Euclid: 5 June 2009

https://projecteuclid.org/euclid.tjm/1244208946

Digital Object Identifier
doi:10.3836/tjm/1244208946

Mathematical Reviews number (MathSciNet)
MR1908223

Zentralblatt MATH identifier
1019.12002

#### Citation

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. https://projecteuclid.org/euclid.tjm/1244208946

#### References

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• 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.