论文标题
计算树木产品中的格子
Counting lattices in products of trees
论文作者
论文摘要
一组宝马学位$（m，n）$是一个集团，它只是在两块普通树的$ m $ $ m $和$ n $的产品的顶点进行过渡。我们表明，对于$（Mn）^{αmn} $和$（Mn）^{βMn} $，对于$ 0 <α<β$，$（mn）^{αmn} $之间的可相称类别的$（m，n）$的可相称类别的数量。实际上，我们证明了几乎简单的宝马组的范围相同。我们为BMW $ $（M，N）$引入了一个随机模型，并表明该模型中几乎可以肯定的是一个随机的BMW组，这是不可还原的，并且在遗传上是无限的。
A BMW group of degree $(m,n)$ is a group that acts simply transitively on vertices of the product of two regular trees of degrees $m$ and $n$. We show that the number of commensurability classes of BMW groups of degree $(m,n)$ is bounded between $(mn)^{αmn}$ and $(mn)^{βmn}$ for some $0<α<β$. In fact, we show that the same bounds hold for virtually simple BMW groups. We introduce a random model for BMW groups of degree $(m,n)$ and show that asymptotically almost surely a random BMW group in this model is irreducible and hereditarily just-infinite.
