Locally minimal topological groups 2 |
| |
Authors: | Lydia Außenhofer |
| |
Institution: | a Matematisch-Geographische Fakultät, Katholische Universität Eichstätt/Ingolstadt, Germany b Departamento de Física y Matemática Aplicada, Universidad de Navarra, Spain c Dipartimento di Matematica e Informatica, Università di Udine, Italy d Departamento de Métodos Matemáticos y de Representación, Universidad de A Coruña, Spain |
| |
Abstract: | We continue in this paper the study of locally minimal groups started in Außenhofer et al. (2010) 4]. The minimality criterion for dense subgroups of compact groups is extended to local minimality. Using this criterion we characterize the compact abelian groups containing dense countable locally minimal subgroups, as well as those containing dense locally minimal subgroups of countable free-rank. We also characterize the compact abelian groups whose torsion part is dense and locally minimal. We call a topological group G almost minimal if it has a closed, minimal normal subgroup N such that the quotient group G/N is uniformly free from small subgroups. The class of almost minimal groups includes all locally compact groups, and is contained in the class of locally minimal groups. On the other hand, we provide examples of countable precompact metrizable locally minimal groups which are not almost minimal. Some other significant properties of this new class are obtained. |
| |
Keywords: | Locally minimal group Minimal group Locally essential subgroup Essential subgroup Almost minimal group GTG set Locally GTG group Group without small subgroups Locally quasi-convex group |
本文献已被 ScienceDirect 等数据库收录! |
|