论文标题
有限生成的组的定量Neumann引理
A quantitative Neumann lemma for finitely generated groups
论文作者
论文摘要
我们研究有限生成的组的coset覆盖功能$ \ mathfrak {c}（r）$：覆盖半径$ r $的球所需的无限索引子组的coset数。我们表明，$ \ mathfrak {c}（r）$至少是所有组的$ \ sqrt {r} $。此外，我们表明$ \ mathfrak {c}（r）$对于包括几乎是nilpotent和polycyclic组在内的一类符合组的类别是线性的，对于属性（t）组，它是指数的。
We study the coset covering function $\mathfrak{C}(r)$ of a finitely generated group: the number of cosets of infinite index subgroups needed to cover the ball of radius $r$. We show that $\mathfrak{C}(r)$ is of order at least $\sqrt{r}$ for all groups. Moreover, we show that $\mathfrak{C}(r)$ is linear for a class of amenable groups including virtually nilpotent and polycyclic groups, and that it is exponential for property (T) groups.
