On omega-categorical groups and rings of finite burden

TL;DR

This paper explores the structure of omega-categorical groups and rings with finite burden, establishing their near-abelian or near-nilpotent nature, and extends results to NTP2 rings.

Contribution

It characterizes omega-categorical groups and rings of finite burden, showing they are virtually finite-by-abelian or finite-by-null, and proves NTP2 rings are virtually nilpotent.

Findings

Omega-categorical groups of finite burden are virtually finite-by-abelian.

Omega-categorical rings of finite burden are virtually finite-by-null.

NTP2 rings are virtually nilpotent.

Abstract

An $\omega$-categorical group of finite burden is virtually finite-by-abelian; an $\omega$-categorical ring of finite burden is virtually finite-by-null; an $\omega$-categorical NTP2 ring is virtually nilpotent.