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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.19554 |
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Table of Contents:
- 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 $H$.