On the average size of $3$-torsion in class groups of $C_2 \wr H$-extensions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929451091099648 |
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| author | Iskander, Jonas Iyer, Hari R. |
| author_facet | Iskander, Jonas Iyer, Hari R. |
| 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 $H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the average size of $3$-torsion in class groups of $C_2 \wr H$-extensions Iskander, Jonas Iyer, Hari R. Number Theory Group Theory 11R29 (Primary) 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 $H$. |
| title | On the average size of $3$-torsion in class groups of $C_2 \wr H$-extensions |
| topic | Number Theory Group Theory 11R29 (Primary) |
| url | https://arxiv.org/abs/2407.19554 |