%0 Journal Article
%T $3$-class field towers of exact length $3$
%A MIchael R. Bush
%A Daniel C. Mayer
%J Mathematics
%D 2013
%I arXiv
%X 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 $p$.
%U http://arxiv.org/abs/1312.0251v1