Near full groups of bounded type, \rom2

2026/07/29 by Zheng Kuang
Mathematics · #math.DS #math.GR

paper · pdf

Part II of a two-part series; Part I: arXiv:2607.25729

arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

We give sufficient conditions for a group of bounded type to contain the AF alternating group. We axiomatize the containment process through alternating data, diagonal inheritance, propagation by selectors, and bounded absorption. We also isolate a class of fragmentations that produce selectors. As an application, we show that a fragmentation group of the modified Fabrykowski--Gupta group contains the AF alternating group, has absorption delay at most 2, and has parity completion equal to its topological full group.

Citations

• Growth of finitely generated subgroups of the topological full groups of inverse semigroups of bounded type
• Growth of groups with incompressible elements, I
• Substitutional subshifts and growth of groups
• Palindromic subshifts and simple periodic groups of intermediate growth
• Simple groups of dynamical origin
• Self-similar groups and topological dimension

Related

• Near full groups of bounded type, \rom1
• On the global breadth of finite groups with nontrivial partitions
• Stabilizers, groups with f-generics in NTP2 and PRC fields
• Irreducible restrictions of representations of alternating groups in small characteristics: Reduction theorems
• Permutation groups with restricted stabilizers