---
_id: '34839'
abstract:
- lang: eng
  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.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Jiuya
  full_name: Wang, Jiuya
  last_name: Wang
citation:
  ama: 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>
  apa: 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>
  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={<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} }'
  chicago: '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>.'
  ieee: '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>.'
  mla: 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>.
  short: J. Klüners, J. Wang, Proceedings of the American Mathematical Society 150
    (2022) 2793–2805.
date_created: 2022-12-22T10:47:01Z
date_updated: 2023-03-06T08:47:42Z
department:
- _id: '102'
doi: 10.1090/proc/15882
external_id:
  arxiv:
  - '2003.12161 '
intvolume: '       150'
issue: '7'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
page: 2793-2805
publication: Proceedings of the American Mathematical Society
publication_identifier:
  issn:
  - 0002-9939
  - 1088-6826
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois
  group
type: journal_article
user_id: '93826'
volume: 150
year: '2022'
...