论文标题
在分支和弱分支组中无限指数的最大亚组上
On maximal subgroups of infinite index in branch and weakly branch groups
论文作者
论文摘要
我们将最初由Pervova开发的技术工具推广到Grigorchuk和GGS组中最大亚组的研究，以满足自然状况的所有弱分支组，尤其是所有分支组。然后，我们使用此工具来证明分支组的每个无限索引的每个最大亚组也是分支组。作为此结果的进一步应用，我们表明大教堂组的每个最大亚组都是有限指数。
We generalise a technical tool, originally developed by Pervova for the study of maximal subgroups in Grigorchuk and GGS groups, to all weakly branch groups satisfying a natural condition, and in particular to all branch groups. We then use this tool to prove that every maximal subgroup of infinite index of a branch group is also a branch group. As a further application of this result, we show that every maximal subgroup of the Basilica group is of finite index.
