most recent 30 from http://mathoverflow.net 2013-05-23T06:01:17Z http://mathoverflow.net/feeds/user/21330 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/88242/about-kummer-theory unknown (google) 2012-02-11T22:57:20Z 2012-04-08T11:22:00Z

<p>In Kummer Theory, we always need the assumption that $a\not\in K^{\times n}$. For the local case, we can use the structure theorem of $K^{\times}$ to check this assumption. But in general, how can we check this condition?</p> <p>For example, how to check $p\not\in K^{\times p}$, where $K=\mathbb{Q}(\mu_{p^\infty})$ the rational number adjoining all the pth power roots of unity.</p>

http://mathoverflow.net/questions/88242/about-kummer-theory 2012-02-11T23:48:33Z 2012-02-11T23:48:33Z

So does it mean we do not have $Gal(K(\sqrt[p^\infty]{p})/K)\cong \mathbb{Z}_p$ for general $p$?