On generic polynomials for the modular 2-groups

被引：2

作者：

Rikuna, Y ^{[1
]}

机构：

[1] Waseda Univ, Dept Math Sci, Shinjuku Ku, Tokyo 1698555, Japan

来源：

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2002年 / 78卷 / 03期

关键词：

inverse Galois problem; Noether's problem; generic polynomials; modular; 2-groups;

D O I：

10.3792/pjaa.78.33

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a generic polynomial for Mod(2n+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 Mod(2n+2)-extension L/K with K superset of k, #K = infinity by specialization of the parameters. Moreover, we derive a new generic polynomial for the cyclic group of order 2(n+1) from our construction.

引用

页码：33 / 35

页数：3