$3$-class field towers of exact length $3$

MIchael R. Bush; Daniel C. Mayer

$3$-class field towers of exact length $3$

Number Theory 2013-12-03 v1 Group Theory

Authors: MIchael R. Bush , Daniel C. Mayer

Abstract

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 $p$ .

Keywords

class field towers hilbert class fields p-group generation algorithm imaginary quadratic fields 3-class groups finite p-class towers

Cite

@article{arxiv.1312.0251,
  title  = {$3$-class field towers of exact length $3$},
  author = {MIchael R. Bush and Daniel C. Mayer},
  journal= {arXiv preprint arXiv:1312.0251},
  year   = {2013}
}

Comments

8 pages

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