论文标题
右角Artin组在扩展图上的作用的酰基。
Acylindricity of the action of right-angled Artin groups on extension graphs
论文作者
论文摘要
众所周知，右角Artin组在其扩展图上的作用是酰基的，因为一对遥远点的所谓$ r $ $ quasi-stabilizer的基数在上面由$ r $的函数界定。基数的已知上限是$ r $的指数函数。在本文中，我们表明，$ r $ quasi-stabilizer是循环组的子集，其基数在上面由$ r $的线性函数界定。这是通过探索组元素的晶格理论特性，研究力量前缀并扩展了准根的独特性从单词长度到星长的独特性来完成。我们还改善了其延伸图上直角artin组的最小渐近翻译长度的已知下限。
The action of a right-angled Artin group on its extension graph is known to be acylindrical because the cardinality of the so-called $r$-quasi-stabilizer of a pair of distant points is bounded above by a function of $r$. The known upper bound of the cardinality is an exponential function of $r$. In this paper we show that the $r$-quasi-stabilizer is a subset of a cyclic group and its cardinality is bounded above by a linear function of $r$. This is done by exploring lattice theoretic properties of group elements, studying prefixes of powers and extending the uniqueness of quasi-roots from word length to star length. We also improve the known lower bound for the minimal asymptotic translation length of a right angled Artin group on its extension graph.
