论文标题
由共轭定义的组上的粗糙结构
Coarse structures on groups defined by conjugations
论文作者
论文摘要
对于一个$ g $，我们用$ \ stackrel {\ leftrightArrow} {g} $ $ g $上的粗空间，带有基本$ \ {\ {（x，y）\ in G \ times g：y in x^f \}： \ {z^{ - 1} xz：z \ in f \} $。我们的目标是探索$ g $的代数属性与$ \ stackrel {\ leftrightArrow} {g} $的渐近属性之间的相互作用。特别是，我们表明$ asdim \ \ stackrel {\ leftrightArrow} {g} = 0 $ i时，仅当$ g / z_g $是本地有限的，$ z_g $是$ g $的中心。对于无限的$ g $，当$ g $是dedekind组时，$ g $的子组的粗糙空间是离散的。
For a group $G$, we denote by $\stackrel{\leftrightarrow}{G}$ the coarse space on $G$ endowed with the coarse structure with the base $\{\{ (x,y)\in G\times G: y\in x^F \} : F \in [G]^{<ω} \}$, $x^F = \{z^{-1} xz : z\in F \}$. Our goal is to explore interplays between algebraic properties of $G$ and asymptotic properties of $\stackrel{\leftrightarrow}{G}$. In particular, we show that $asdim \ \stackrel{\leftrightarrow}{G} = 0$ if and only if $G / Z_G$ is locally finite, $Z_G$ is the center of $G$. For an infinite group $G$, the coarse space of subgroups of $G$ is discrete if and only if $G$ is a Dedekind group.
