On Malle’s conjecture for nilpotent groups

Transactions of the American Mathematical Society, Series B Pub Date : 2023-03-03 DOI:10.1090/btran/140

P. Koymans, Carlo Pagano

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引用次数: 6

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.

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幂零群的Malle猜想

本文提出了一个研究Malle猜想强形式的抽象框架[J]。数论92 (2002)，pp. 315-329;实验。数学，13 (2004)，pp. 129-135]幂零群G G的正则表示。然后用这个框架证明了任意幂零群G G的Malle猜想的强形式，使得p阶的所有元素都是中心的，其中p阶是# G \# G的最小素数，我们还给出了任意幂零群G G紧于对数因子的上界，以及所有p阶元素成对交换时紧于常数因子的上界。最后，在幂零群正则表示的情况下，给出了支持Malle猜想的一个新的启发式论证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Transactions of the American Mathematical Society, Series B

CiteScore

1.70

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0.00%

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