论文标题
可解决的组，希尔伯特·史克米特稳定性和密集的周期性措施的字符
Characters of solvable groups, Hilbert-Schmidt stability and dense periodic measures
论文作者
论文摘要
我们研究了Metabelian和多环类群的特征理论。它用于通过Hadwin和Shulman的字符理论标准来研究Hilbert-Schmidt的稳定性。紧凑型阿伯利亚群体的稳定性和动力学之间存在密切的联系。依靠这一点，我们推断出有限生成的几乎没有尼尔氏群，自由的metabelian群体，灯塔组以及上三角形组上的某些代数整数环是希尔伯特·史密斯（Hilbert-Schmidt）的稳定。
We study the character theory of metabelian and polycyclic groups. It is used to investigate Hilbert-Schmidt stability via the character-theoretic criterion of Hadwin and Shulman. There is a close connection between stability and dynamics of automorphisms of compact abelian groups. Relying on this, we deduce that finitely generated virtually nilpotent groups, free metabelian groups, lamplighter groups as well as upper triangular groups over certain rings of algebraic integers are Hilbert-Schmidt stable.
