有限生成群的定量诺依曼定理

IF 0.8 2区数学 Q2 MATHEMATICS

Israel Journal of Mathematics Pub Date : 2024-04-24 DOI:10.1007/s11856-024-2617-x

Elia Gorokhovsky, Nicolás Matte Bon, Omer Tamuz

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引用次数: 0

摘要

我们研究了一个无限有限生成群的余集覆盖函数ℭ(r)：覆盖半径为 r 的球所需的无限索引子群的余集数。我们证明了ℭ(r)对于所有群都至少是 \(s\qrt{r}\)阶。此外，我们还证明了ℭ(r)对于一类可合并群（包括几乎无穷群和多环群）来说是线性的，而对于性质（T）群来说是指数级的。

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A quantitative Neumann lemma for finitely generated groups

We study the coset covering function ℭ(r) of an infinite, finitely generated group: the number of cosets of infinite index subgroups needed to cover the ball of radius r. We show that ℭ(r) is of order at least \(\sqrt{r}\) for all groups. Moreover, we show that ℭ(r) is linear for a class of amenable groups including virtually nilpotent and polycyclic groups, and that it is exponential for property (T) groups.

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来源期刊

Israel Journal of Mathematics 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.