{"year":"2022","date_updated":"2023-03-06T08:47:42Z","department":[{"_id":"102"}],"page":"2793-2805","volume":150,"publisher":"American Mathematical Society (AMS)","publication_status":"published","_id":"34839","publication_identifier":{"issn":["0002-9939","1088-6826"]},"issue":"7","doi":"10.1090/proc/15882","language":[{"iso":"eng"}],"abstract":[{"text":"We describe the relations among the ℓ-torsion conjecture, a conjecture of Malle giving an upper bound for the number of extensions, and the discriminant multiplicity conjecture. We prove that the latter two conjectures are equivalent in some sense. Altogether, the three conjectures are equivalent for the class of solvable groups. We then prove the ℓ-torsion conjecture for ℓ-groups and the other two conjectures for nilpotent groups.","lang":"eng"}],"title":"ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group","keyword":["Applied Mathematics","General Mathematics"],"status":"public","intvolume":" 150","external_id":{"arxiv":["2003.12161 "]},"citation":{"apa":"Klüners, J., & Wang, J. (2022). ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group. Proceedings of the American Mathematical Society, 150(7), 2793–2805. https://doi.org/10.1090/proc/15882","ama":"Klüners J, Wang J. ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group. Proceedings of the American Mathematical Society. 2022;150(7):2793-2805. doi:10.1090/proc/15882","short":"J. Klüners, J. Wang, Proceedings of the American Mathematical Society 150 (2022) 2793–2805.","bibtex":"@article{Klüners_Wang_2022, title={ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group}, volume={150}, DOI={10.1090/proc/15882}, number={7}, journal={Proceedings of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={Klüners, Jürgen and Wang, Jiuya}, year={2022}, pages={2793–2805} }","chicago":"Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group of Number Fields with an ℓ-Group as Galois Group.” Proceedings of the American Mathematical Society 150, no. 7 (2022): 2793–2805. https://doi.org/10.1090/proc/15882.","mla":"Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group of Number Fields with an ℓ-Group as Galois Group.” Proceedings of the American Mathematical Society, vol. 150, no. 7, American Mathematical Society (AMS), 2022, pp. 2793–805, doi:10.1090/proc/15882.","ieee":"J. Klüners and J. Wang, “ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group,” Proceedings of the American Mathematical Society, vol. 150, no. 7, pp. 2793–2805, 2022, doi: 10.1090/proc/15882."},"date_created":"2022-12-22T10:47:01Z","author":[{"full_name":"Klüners, Jürgen","first_name":"Jürgen","id":"21202","last_name":"Klüners"},{"last_name":"Wang","full_name":"Wang, Jiuya","first_name":"Jiuya"}],"user_id":"93826","publication":"Proceedings of the American Mathematical Society","type":"journal_article"}