标题： 从树的乘积中得到的半双射性 显示英文标题

标题： Semidualities from products of trees

摘要： 设$K$为特征为$p$的全局函数域，令$\Gamma$为相对于$K$定义的算术群的一个有限指数子群，并且$\Gamma$的任何挠元都是$p$-挠元。 我们定义半对偶群，并证明当$\Gamma$在树的乘积上作为格作用时，$\Gamma$是一个$\mathbb{Z}[1/p]$-半对偶群。 我们还给出了其他半对偶群的例子，包括灯笼夫群、Diestel-Leader 群和有限群的可数和。 显示英文摘要

摘要： Let $K$ be a global function field of characteristic $p$, and let $\Gamma$ be a finite-index subgroup of an arithmetic group defined with respect to $K$ and such that any torsion element of $\Gamma$ is a $p$-torsion element. We define semiduality groups, and we show that $\Gamma$ is a $\mathbb{Z}[1/p]$-semiduality group if $\Gamma$ acts as a lattice on a product of trees. We also give other examples of semiduality groups, including lamplighter groups, Diestel-Leader groups, and countable sums of finite groups.