On Malle’s conjecture for nilpotent groups

Author:

Koymans Peter,Pagano Carlo

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 G in their regular representation. This framework is then used to prove the strong form of Malle’s conjecture for any nilpotent group G G such that all elements of order p p are central, where p p is the smallest prime divisor of # G \# G .

We also give an upper bound for any nilpotent group G G tight up to logarithmic factors, and tight up to a constant factor in case all elements of order p p pairwise commute. Finally, we give a new heuristical argument supporting Malle’s conjecture in the case of nilpotent groups in their regular representation.

Funder

University of Michigan

Publisher

American Mathematical Society (AMS)

Subject

General Earth and Planetary Sciences,General Environmental Science

Reference53 articles.

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