Groups admitting no non-discrete locally minimal group topologies

摘要

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. This answers a question posed by D. Dikranjan and M. Megrelishvili in 7, in particular, a question posed by L. Aussenhofer, M. Jesus Chasco, D. Dikranjan and X. Dominguez in 1. Moreover, we give a necessary and sufficient condition for a bounded abelian group admits a non discrete locally minimal group topology. (C) 2020 Elsevier B.V. All rights reserved.