论文标题
组合共轭的动态方法
The dynamical approach to the conjugacy in groups
论文作者
论文摘要
给定一个离散的组$ g $，我们可以通过$ g $上的所有Ultrafters组合$ g^\ ast =βg\ setminus g $，并将所有超级滤器组合在一起。 conjugations $（g，x）\ mapsto g^{ - 1} xg $在$ g $上的操作$ g $诱导了$ g $的动作，$ g^\ ast $ by $ g^\ ast $ by $（g，p）\ mapsto p^g $，$ p^g $，$ p^g = = \ = \ = \ {g^{g^{g^{ - 1} pg { - 1} pg：pg \ p \^$} $。我们研究$ g $的代数属性与$（g，g^\ ast）$的动态属性之间的相互作用。特别是，我们表明$ p^g $对于g^\ ast $中的每个$ p \ in g^\ ast $中的每个$ p^g $，并且仅当$ g $的可容纳$ g $是有限的。
Given a discrete group $G$, we identify the Stone-$\check C$ech compactification $βG$ with the set of all ultrafilters on $G$ and put $G^\ast =βG\setminus G$. The action $G$ on $G$ by the conjugations $(g,x)\mapsto g^{-1}xg$ induces the action of $G$ on $G^\ast$ by $(g, p)\mapsto p^g $, $p^g = \{ g^{-1} Pg: P\in p\}$. We study interplays between the algebraic properties of $G$ and the dynamical properties of $(G, G^\ast)$. In particular, we show that $p^G$ is finite for each $p\in G^\ast$ if and only if the commutant of $G$ is finite.
