@inproceedings{6110845747164ae38294adf73fd02acf,
title = "Quasi-minimal Abelian groups",
abstract = "An abelian group \$G\$ is said to be quasi-minimal (purely quasi-minimal, directly quasi-minimal) if it is isomorphic to all its subgroups (pure subgroups, direct summands, respectively) of the same cardinality as \$G\$. Obviously quasi-minimality implies pure quasi-minimality which in turn implies direct quasi-minimality, but we show that neither converse implication holds. We obtain a complete characterisation of quasi-minimal groups. In the purely quasi-minimal case, assuming GCH, a complete characterisation is also established. An independence result is proved for directly quasi-minimal groups.",
keywords = "abelian group, quasi-minimal, purely quasi-minimal, directly quasi-minimal, GCH, independence result",
author = "Brenda Goldsmith and S. {\'O}h{\'o}g{\'a}in and S. Wallutis",
year = "2004",
month = aug,
doi = "10.1090/S0002-9939-04-07065-0",
language = "English",
volume = "132",
series = "Proceedings of the American Mathematical Society",
publisher = "American Mathematical Society",
pages = "2185--2195",
booktitle = "Proceedings of the American Mathematical Society",
edition = "8",
}