Aleph-zero-categorical groups and their completions

TL;DR

This paper explores how embedding a countably categorical group into a locally compact topological group reveals connections between topological properties and the structure of definable subgroups.

Contribution

It introduces a method to embed countably categorical groups into locally compact groups and analyzes the relationship between their topological and algebraic structures.

Findings

Topological properties of c(G) relate to definable subgroups of G

Embedding reveals structural insights into countably categorical groups

Connections between model-theoretic and topological properties established

Abstract

We embed a countably categorical group G into a locally compact group c(G) with a non-trivial topology and study how topological properties of c(G) are connected with the structure of definable subgroups of G.