论文标题
多性小组的共轭类
Conjugacy classes of polyspinal groups
论文作者
论文摘要
脊柱组和多GGS组都是众所周知的Grigorchuk-Gupta-Sidki（GGS-）组的概括。在这里，我们提供了脊柱组结合的必要条件，并为多GGS组建立了必要的条件。我们还引入了两个类别的自然常见概括，我们称之为多细分组。我们的结果使我们能够对Bartholdi，Grigorchuk和Sunik的问题给出负面答案，该问题是关于每个有限生成的分支组是否对弱分支的脊柱组同构。
Spinal groups and multi-GGS groups are both generalisations of the well-known Grigorchuk-Gupta-Sidki (GGS-)groups. Here we give a necessary condition for spinal groups to be conjugate, and we establish a necessary and sufficient condition for multi-GGS groups to be conjugate. We also introduce a natural common generalisation of both classes, which we call polyspinal groups. Our results enable us to give a negative answer to a question of Bartholdi, Grigorchuk and Sunik, on whether every finitely generated branch group is isomorphic to a weakly branch spinal group.
