On Malle’s conjecture for nilpotent groups

Koymans, Peter; Pagano, Carlo

doi:10.1090/btran/140

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

On Malle’s conjecture for nilpotent groups

MPS-Authors

/persons/resource/persons262194

Koymans, Peter
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons248540

Pagano, Carlo
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1090/btran/140
(Publisher version)

https://doi.org/10.48550/arXiv.2103.17223
(Preprint)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

Koymans-Pagano_On Malle’s conjecture for nilpotent groups_2023.pdf
(Publisher version), 497KB

Supplementary Material (public)

There is no public supplementary material available

Citation

Koymans, P., & Pagano, C. (2023). On Malle’s conjecture for nilpotent groups. Transactions of the American Mathematical Society. Series B, 10, 310-354. doi:10.1090/btran/140.

Cite as: https://hdl.handle.net/21.11116/0000-000D-1EB3-8

Abstract

We develop an abstract framework for studying the strong form
of Malle’s conjecture [J. Number Theory 92 (2002), pp. 315–329; Experiment.
Math. 13 (2004), pp. 129–135] for nilpotent groups G in their regular rep-
resentation. This framework is then used to prove the strong form of Malle’s
conjecture for any nilpotent group G such that all elements of order p are
central, where p is the smallest prime divisor of #G.
We also give an upper bound for any nilpotent group G tight up to loga-
rithmic factors, and tight up to a constant factor in case all elements of order
p pairwise commute. Finally, we give a new heuristical argument supporting
Malle’s conjecture in the case of nilpotent groups in their regular representation.