Osaka Journal of Mathematics

On the existence of unramified $p$-extensions with prescribed Galois group

Akito Nomura

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We shall prove that for any finite $p$-group $G$, there exists an elementary abelian $p$-extension $k/\mathbf{Q}$ and an unramified extension $K/k$ such that the Galois group $\mathrm{Gal}(K/k)$ is isomorphic to $G$.

Article information

Osaka J. Math., Volume 47, Number 4 (2010), 1159-1165.

First available in Project Euclid: 20 December 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 12F12: Inverse Galois theory 11R29: Class numbers, class groups, discriminants


Nomura, Akito. On the existence of unramified $p$-extensions with prescribed Galois group. Osaka J. Math. 47 (2010), no. 4, 1159--1165.

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