article published Jürgen Klüners author 21202 Jiuya Wang author 102 department 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. American Mathematical Society (AMS)2022 eng Applied MathematicsGeneral Mathematics 0002-9939 1088-6826 2003.12161 10.1090/proc/15882 15072793-2805 Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group of Number Fields with an ℓ-Group as Galois Group.” <i>Proceedings of the American Mathematical Society</i>, vol. 150, no. 7, American Mathematical Society (AMS), 2022, pp. 2793–805, doi:<a href="https://doi.org/10.1090/proc/15882">10.1090/proc/15882</a>. @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={<a href="https://doi.org/10.1090/proc/15882">10.1090/proc/15882</a>}, 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} } Klüners J, Wang J. ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group. <i>Proceedings of the American Mathematical Society</i>. 2022;150(7):2793-2805. doi:<a href="https://doi.org/10.1090/proc/15882">10.1090/proc/15882</a> J. Klüners and J. Wang, “ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group,” <i>Proceedings of the American Mathematical Society</i>, vol. 150, no. 7, pp. 2793–2805, 2022, doi: <a href="https://doi.org/10.1090/proc/15882">10.1090/proc/15882</a>. Klüners, J., &#38; Wang, J. (2022). ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group. <i>Proceedings of the American Mathematical Society</i>, <i>150</i>(7), 2793–2805. <a href="https://doi.org/10.1090/proc/15882">https://doi.org/10.1090/proc/15882</a> Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group of Number Fields with an ℓ-Group as Galois Group.” <i>Proceedings of the American Mathematical Society</i> 150, no. 7 (2022): 2793–2805. <a href="https://doi.org/10.1090/proc/15882">https://doi.org/10.1090/proc/15882</a>. J. Klüners, J. Wang, Proceedings of the American Mathematical Society 150 (2022) 2793–2805. 348392022-12-22T10:47:01Z2023-03-06T08:47:42Z