On the average size of \(3\)-torsion in class groups of \(C_2 \wr H\)-extensions

On the average size of \(3\)-torsion in class groups of \(C_2 \wr H\)-extensions

The Cohen-Lenstra-Martinet heuristics lead one to conjecture that the average size of the \(p\)-torsion in class groups of \(G\)-extensions of a number field is finite. In a 2021 paper, Lemke Oliver, Wang, and Wood proved this conjecture in the case of \(p = 3\) for permutation groups \(G\) of the f...

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Veröffentlicht in:arXiv.org 2024-08
Hauptverfasser: Iskander, Jonas, Iyer, Hari R
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description The Cohen-Lenstra-Martinet heuristics lead one to conjecture that the average size of the \(p\)-torsion in class groups of \(G\)-extensions of a number field is finite. In a 2021 paper, Lemke Oliver, Wang, and Wood proved this conjecture in the case of \(p = 3\) for permutation groups \(G\) of the form \(C_2 \wr H\) for a broad family of permutation groups \(H\), including most nilpotent groups. However, their theorem does not apply for some nilpotent groups of interest, such as \(H = C_5\). We extend their results to prove that the average size of \(3\)-torsion in class groups of \(C_2 \wr H\)-extensions is finite for any nilpotent group \(H\).
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title On the average size of \(3\)-torsion in class groups of \(C_2 \wr H\)-extensions
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