On groups whose subgroups are closed in the profinite topology

A group is called extended residually finite (ERF) if every subgroup is closed in the profinite topology. The ERF-property is studied for nilpotent groups, soluble groups, locally finite groups and FC-groups. A complete characterization is given of FC-groups which are ERF.

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Bibliographic Details
Published in:Journal of pure and applied algebra 2009-04, Vol.213 (4), p.421-429
Main Authors: Robinson, Derek J.S., Russo, Alessio, Vincenzi, Giovanni
Format: Article
Language:English
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Summary:A group is called extended residually finite (ERF) if every subgroup is closed in the profinite topology. The ERF-property is studied for nilpotent groups, soluble groups, locally finite groups and FC-groups. A complete characterization is given of FC-groups which are ERF.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2008.07.015