---
_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. *Proceedings of the American Mathematical Society*.
2022;150(7):2793-2805. doi:10.1090/proc/15882
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
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.'
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.'
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.
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'
...