论文标题
主树上的GGS组：分支结构
GGS-groups over primary trees: Branch structures
论文作者
论文摘要
我们研究了主要树木的Grigorchuk-Gupta-Sidki组（GGS组）的分支结构，即Prime $ p $的定期植根于$ p^n $的生根树。除了$ p = 2 $的一小部分例外外，我们证明所有这些小组都是$ g''$的弱规则分支。此外，在大多数情况下，它们实际上是$γ_3（g）$的常规分支。这是关于周期性GGS组对原始树和一般GGS组的先前已知结果的显着扩展。我们还表明，与情况一样，$ n = 1 $，常数向量生成的GGS组不是分支。
We study branch structures in Grigorchuk-Gupta-Sidki groups (GGS-groups) over primary trees, that is, regular rooted trees of degree $p^n$ for a prime $p$. Apart from a small set of exceptions for $p=2$, we prove that all these groups are weakly regular branch over $G''$. Furthermore, in most cases they are actually regular branch over $γ_3(G)$. This is a significant extension of previously known results regarding periodic GGS-groups over primary trees and general GGS-groups in the case $n=1$. We also show that, as in the case $n=1$, a GGS-group generated by a constant vector is not branch.
