论文标题
差异性细菌群的代数特性
Algebraic properties of the group of germs of diffeomorphisms
论文作者
论文摘要
我们建立了组$ \ mathrm {diff}（\ mathbb {c}^n，0）$的一些代数属性。例如，我们描述了$ \ mathrm {diff}（\ mathbb {c}^n，0）$的换向器，但也证明了$ \ mathrm {diff}的任何有限生成的亚组因此，我们获得了嵌入$ \ mathrm {diff}（\ mathbb {c}^n，0）$的组的一些约束。我们表明，$ \ wideHat {\ mathrm {diff}}（\ mathbb {c}^n，0）$是一个霍普里安组，而$ \ mathrm {diff}（\ mathbb {c}^n，0）$不是共求人。我们以$ \ wideHat {\ mathrm {diff}}}（\ MathBb {C}，0）$和$ \ MathRM {diff}（\ MathBb {c}，0）$的自动形态组的描述结束。
We establish some algebraic properties of the group $\mathrm{Diff}(\mathbb{C}^n,0)$ of germs of analytic diffeomorphisms of $\mathbb{C}^n$, and its formal completion $\widehat{\mathrm{Diff}}(\mathbb{C}^n,0)$. For instance we describe the commutator of $\mathrm{Diff}(\mathbb{C}^n,0)$, but also prove that any finitely generated subgroup of $\mathrm{Diff}(\mathbb{C}^n,0)$ is residually finite; we thus obtain some constraints of groups that embed into $\mathrm{Diff}(\mathbb{C}^n,0)$. We show that $\widehat{\mathrm{Diff}}(\mathbb{C}^n,0)$ is an Hopfian group, and that $\mathrm{Diff}(\mathbb{C}^n,0)$ and $\widehat{\mathrm{Diff}}(\mathbb{C}^n,0)$ are not co-Hopfian. We end by the description of the automorphisms groups of $\widehat{\mathrm{Diff}}(\mathbb{C},0)$, and $\mathrm{Diff}(\mathbb{C},0)$.
