Kronecker-Weber plus epsilon
Kronecker-Weber plus epsilon
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DOI：
10.1215/s0012-7094-02-11432-x
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发表时间：
2001-03
影响因子：
2.5
通讯作者：
G. Anderson
中科院分区：
文献类型：
--
作者：
G. Anderson
我们说一个群几乎是阿贝尔群，如果每个换位子都是中心的且平方于单位元。现在设G是复数域中有理数域Q的代数闭包的伽罗瓦群。设Gab ~+是G对几乎阿贝尔profinite群的连续同态泛的商，Qab ~+ /Q是相应的Galois扩张.证明了Qab +是由单位根、有理素数的四次根和某些代数正弦单项式的平方根生成的。本文的灵感来自于P. Das和S.徐
We say that a group is 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 Q of rational numbers in the field of complex numbers. Let Gab + be the quotient of G universal for continuous homomorphisms to almost abelian profinite groups and let Qab + /Q be the corresponding Galois extension. We prove that Qab + is generated by the roots of unity, the fourth roots of the rational primes and the square roots of certain algebraic sine-monomials. The inspiration for the paper came from recent studies of algebraic Γ-monomials by P. Das and by S. Seo.