Countably infinite bounded abelian groups admit no non-discrete locally minimal group topologies

TL;DR

This paper proves that countably infinite bounded abelian groups cannot have non-discrete locally minimal topologies, implying such groups only admit the discrete topology under these conditions.

Contribution

It establishes that countably infinite bounded abelian groups have no non-discrete locally minimal topologies, a new result in the topology of abelian groups.

Findings

Only discrete topology exists for these groups

Non-discrete locally minimal topologies are impossible

Results apply to groups with nG=0 for some n

Abstract

In this note we show that if $G$ is a countably infinite abelian group such that $nG=0$ for some integer $n$, then the only locally minimal group topology on $G$ is the discrete one.