On S3-extensions with infinite class field tower
classification
🧮 math.NT
keywords
classfieldinfinitetowerapplicationauthorconstructdiscriminant
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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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