
arXiv: 2103.17223
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.
nilpotent group, Mathematics - Number Theory, 11N37, 11R45, FOS: Mathematics, upper bound, asymptotic, Number Theory (math.NT), Asymptotic results on counting functions for algebraic and topological structures, Other abelian and metabelian extensions, Malle's Conjecture
nilpotent group, Mathematics - Number Theory, 11N37, 11R45, FOS: Mathematics, upper bound, asymptotic, Number Theory (math.NT), Asymptotic results on counting functions for algebraic and topological structures, Other abelian and metabelian extensions, Malle's Conjecture
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