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arXiv · 1308.1572

On S3-extensions with infinite class field tower

Jonah Leshin
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Abstract

We construct a class of $S_3$-extensions of $\Q$ with infinite 3-class field tower in which only three primes ramify. As an application, we obtain an $S_3$-extension of $\Q$ with infinite 3-class field tower with smallest known (to the author) root discriminant among all fields with infinite 3-class field tower.

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Jonah Leshin. 2013-08-08. On S3-extensions with infinite class field tower. https://arxiv.org/abs/1308.1572

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