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Pointwise Bound for $\ell$-torsion in Class Groups II: Nilpotent Extensions

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arxiv 2006.10295 v1 pith:DDHCRAZC submitted 2020-06-18 math.NT math.GR

Jiuya Wang This is my paper · ORCID
classification math.NTmath.GR
keywords everygroupboundclasstorsionextensionintegernilpotent
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abstract

For every finite $p$-group $G_p$ that is non-cyclic and non-quaternion and every positive integer $\ell\neq p$ that is greater than $2$, we prove the first non-trivial bound on $\ell$-torsion in class group of every $G_p$-extension. More generally, for every nilpotent group $G$ where every Sylow-$p$ subgroup $G_p\subset G$ is non-cyclic and non-quaternion, we prove a non-trivial bound on $\ell$-torsion in class group of every $G$-extension for every integer $\ell>1$.

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Cited by 1 Pith paper

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  1. Inductive methods for counting number fields

    math.NT 2025-01 conditional novelty 8.0 of 10

    Introduces a fiber-summation inductive method that proves new cases of Malle's conjecture and gives counterexamples to Malle's predicted exponents for wreath products.

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