Solvable number field extensions of bounded root discriminant

Leshin, Jonah

doi:10.1090/S0002-9939-2013-12015-0

Solvable number field extensions of bounded root discriminant
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by Jonah Leshin

Proc. Amer. Math. Soc. 141 (2013), 3341-3352

DOI: https://doi.org/10.1090/S0002-9939-2013-12015-0

Published electronically: June 14, 2013

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Abstract:

Let $K$ be a number field and $d_K$ the absolute value of the discriminant of $K/\mathbb {Q}$. We consider the root discriminant $d_L^{\frac {1}{[L:\mathbb {Q}]}}$ of extensions $L/K$. We show that for any $N>0$ and any positive integer $n$, the set of length $n$ solvable extensions of $K$ with root discriminant less than $N$ is finite. The result is motivated by the study of class field towers.

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