On \omega-categorical, generically stable groups and rings

TL;DR

This paper proves that -categorical, generically stable groups and rings are structurally close to nilpotent groups and rings, being nilpotent-by-finite, thus advancing understanding of their algebraic classification.

Contribution

It establishes that all -categorical, generically stable groups and rings are nilpotent-by-finite, providing a significant structural characterization in model theory.

Findings

All -categorical, generically stable groups are nilpotent-by-finite.

All -categorical, generically stable rings are nilpotent-by-finite.

The results unify the understanding of algebraic structures under -categoricity and generic stability.

Abstract

We prove that every \omega-categorical, generically stable group is nilpotent-by-finite and that every \omega-categorical, generically stable ring is nilpotent-by-finite.