Weakly maximal subgroups in regular branch groups

作者：Bou Rabee Khalid^*; Leemann Paul Henry; Nagnibeda Tatiana

来源：Journal of Algebra, 2016, 455: 347-357.

DOI：10.1016/j.jalgebra.2016.02.009

• Branch groups
• Weakly maximal subgroups
• Grigorchuk group
• Parabolic subgroups

Let G be a finitely generated regular branch group acting by automorphisms on a regular rooted tree T. It is wellknown that stabilizers of infinite rays in T (aka parabolic subgroups) are weakly maximal subgroups in G, that is, maximal among subgroups of infinite index. We show that, given a finite subgroup Q <= G, G possesses uncountably many automorphism equivalence classes of weakly maximal subgroups containing Q. In particular, for Grigorchuk-Gupta- Sidki type groups this implies that they have uncountably many automorphism equivalence classes of weakly maximal subgroups that are not parabolic.

• 出版日期2016-6-1