group theory

Near full groups of bounded type, \rom{2}

arXiv:2607.26572

summary

The paper provides sufficient conditions for groups of bounded type to contain the AF alternating group, formalizes the containment process, and applies these results to a fragmentation of the modified Fabrykowski–Gupta group.

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 , and has parity completion equal to its topological full group.

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

Topics & keywords

#bounded type groups#AF alternating group#fragmentation groups#Fabrykowski–Gupta group#topological full groupsalternating datadiagonal inheritanceselectorsbounded absorptionabsorption delayparity completion
Near full groups of bounded type, \rom{2} · wovepaper