论文标题
实际上，在自动形态下具有许多轨道有限轨道的nilpotent组
Virtually nilpotent groups with finitely many orbits under automorphisms
论文作者
论文摘要
让$ g $成为一个小组。 $ g $上$ \ aut（g）$的自然动作的轨道称为$ g $的“自动形态轨道”，$ g $的汽车轨道数量用$ω（g）$表示。令$ g $为几乎是nilpotent群体，以便$ω（g）<\ infty $。我们证明$ g = k \ rtimes h $其中$ h $是扭转子组，$ k $是$ g $的无扭矩的nilpotent radicable特征子组。此外，我们证明$ g^{'} = d \ times \ tor（g^{'}）$，其中$ d $是无扭矩的nilpotent radicable特性子组。特别是，如果$ g $的最大正常扭转亚组$τ（g）$是微不足道的，则$ g^{'} $是nilpotent。
Let $G$ be a group. The orbits of the natural action of $\Aut(G)$ on $G$ are called "automorphism orbits" of $G$, and the number of automorphism orbits of $G$ is denoted by $ω(G)$. Let $G$ be a virtually nilpotent group such that $ω(G)< \infty$. We prove that $G = K \rtimes H$ where $H$ is a torsion subgroup and $K$ is a torsion-free nilpotent radicable characteristic subgroup of $G$. Moreover, we prove that $G^{'}= D \times \Tor(G^{'})$ where $D$ is a torsion-free nilpotent radicable characteristic subgroup. In particular, if the maximum normal torsion subgroup $τ(G)$ of $G$ is trivial, then $G^{'}$ is nilpotent.
