MIchael R. Bush, Daniel C. Mayer
Published 2013-12-01Version 1
The $p$-group generation algorithm is used to verify that the Hilbert $3$-class field tower has length $3$ for certain imaginary quadratic fields $K$ with $3$-class group $\mathrm{Cl}_3(K) \cong [3,3]$. Our results provide the first examples of finite $p$-class towers of length $> 2$ for an odd prime $p$.
On the rank of the $2$-class group of $\mathbb{Q}(\sqrt{p}, \sqrt{q},\sqrt{-1})$
Pointwise Bound for $\ell$-torsion in Class Groups II: Nilpotent Extensions
The 2-primary class group of certain hyperelliptic curves
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