论文标题
多项式环的驯服自动形态组（t）和无限的许多交替组商
Tame automorphism groups of polynomial rings with property (T) and infinitely many alternating group quotients
论文作者
论文摘要
我们建立了具有财产（T）的团体的新家庭和无限的许多交替群体商。其中一个由$ \ mathrm {aut}的子组组成（\ mathbf f_ {p} [x_1，\ dots，x_n]）$由合适的驯服自动形态产生。使用$ \ mathrm {aut}的自然动作（\ Mathbf f_ {p} [x_1，\ dots，x_n]）$在$ n $二维仿射空间上构建有限商。结果，我们获得了具有特性（T）和许多交替的组商的Gromov双曲线群的明确演示。我们的建筑还产生了一个明显的无限股东科利（Cayley）的家族，用于交替的$ p^7-1 $的交替$ p^7-1 $的ebayley图表$ 4 $。
We construct new families of groups with property (T) and infinitely many alternating group quotients. One of those consists of subgroups of $\mathrm{Aut}(\mathbf F_{p}[x_1, \dots, x_n])$ generated by a suitable set of tame automorphisms. Finite quotients are constructed using the natural action of $\mathrm{Aut}(\mathbf F_{p}[x_1, \dots, x_n])$ on the $n$-dimensional affine spaces over finite extensions of $\mathbf F_p$. As a consequence, we obtain explicit presentations of Gromov hyperbolic groups with property (T) and infinitely many alternating group quotients. Our construction also yields an explicit infinite family of expander Cayley graphs of degree $4$ for alternating groups of degree $p^7-1$ for any odd prime $p$.
