论文标题
一类重新排列的组总是不会产生的
A Class of Rearrangement Groups that are not Invariably Generated
论文作者
论文摘要
如果存在一个子集$ s \ subseteq g $，则$ g $总是会产生的，这样，对于每一个选择，$ g $ in g $ in g $ for $ s \ in s $ in s $，$ g $由$ \ \ {s^{g_s} \ s \ in s \} $。在[GGJ16] Gelander中，Golan和Juschenko表明，汤普森组$ t $和$ v $并非总是产生。在这里，我们将此结果推广到重排组的较大设置，证明具有一定的传递性能的重排组的任何子组始终不会产生。
A group $G$ is invariably generated if there exists a subset $S \subseteq G$ such that, for every choice $g_s \in G$ for $s \in S$, the group $G$ is generated by $\{ s^{g_s} \mid s \in S \}$. In [GGJ16] Gelander, Golan and Juschenko showed that Thompson groups $T$ and $V$ are not invariably generated. Here we generalize this result to the larger setting of rearrangement groups, proving that any subgroup of a rearrangement group that has a certain transitive property is not invariably generated.
