克罗内克-韦伯加

摘要：

我们说一个群是{ \em几乎阿贝尔}群，如果每个换位子都是中心的且平方于单位元。现在让$G$是复数域中有理数的域$\QQ$的代数闭包的伽罗瓦群。设$G^{\ab+ε}$是$G$对几乎阿贝尔投射有限群同态泛的商，$\QQ^{\ab+ε}/\QQ$是相应的Galois扩张.我们证明了$\QQ^{\ab+ε}$是由单位根、（有理数）素数的四次方根和某些正弦单项式的平方根生成的。本文的灵感来源于P.~ Das and by S.~徐这篇论文发表于Duke Math.J.114（2002）439-475。

英文摘要：

We say that a group is {\em almost abelian} if every commutator is central and squares to the identity. Now let $G$ be the Galois group of the algebraic closure of the field $\QQ$ of rational numbers in the field of complex numbers. Let $G^{\ab+ε}$ be the quotient of $G$ universal for homomorphisms to almost abelian profinite groups and let $\QQ^{\ab+ε}/\QQ$ be the corresponding Galois extension. We prove that $\QQ^{\ab+ε}$ is generated by the roots of unity, the fourth roots of the (rational) prime numbers and the square roots of certain sine-monomials. The inspiration for the paper came from recent studies of algebraic $Γ$-monomials by P.~Das and by S.~Seo. This paper has appeared as Duke Math. J. 114 (2002) 439-475.

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