Open Access
March 2002 On generic polynomials for the modular 2-groups
Yūichi Rikuna
Proc. Japan Acad. Ser. A Math. Sci. 78(3): 33-35 (March 2002). DOI: 10.3792/pjaa.78.33


We construct a generic polynomial for $\mathrm{Mod}_{2^{n+2}}$, the modular 2-group of order $2^{n+2}$, with two parameters over the $2^n$-th cyclotomic field $k$. Our construction is based on an explicit answer for linear Noether's problem. This polynomial, which has a remarkably simple expression, gives every $\mathrm{Mod}_{2^{n+2}}$-extension $L/K$ with $K \supset k$, $\sharp K = \infty$ by specialization of the parameters. Moreover, we derive a new generic polynomial for the cyclic group of order $2^{n+1}$ from our construction.


Download Citation

Yūichi Rikuna. "On generic polynomials for the modular 2-groups." Proc. Japan Acad. Ser. A Math. Sci. 78 (3) 33 - 35, March 2002.


Published: March 2002
First available in Project Euclid: 23 May 2006

zbMATH: 1001.12003
MathSciNet: MR1894898
Digital Object Identifier: 10.3792/pjaa.78.33

Primary: 12F12
Secondary: 13A50

Keywords: generic polynomials , inverse Galois problem , modular 2-groups , Noether's problem

Rights: Copyright © 2002 The Japan Academy

Vol.78 • No. 3 • March 2002
Back to Top