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Quasi-minimal abelian groups
Author(s):
B.
Goldsmith;
S.
Óhógáin;
S.
Wallutis
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2185-2195.
MSC (2000):
Primary 20K99
Posted:
March 24, 2004
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Abstract:
An abelian group  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  . 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.
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Additional Information:
B.
Goldsmith
Affiliation:
School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland
Email:
brendan.goldsmith@dit.ie
S.
Óhógáin
Affiliation:
School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland
Email:
johog@maths.tcd.ie
S.
Wallutis
Affiliation:
Fachbereich 6, Mathematik und Informatik, Universität Essen, 45117 Essen, Germany
Email:
simone.wallutis@uni-essen.de
DOI:
10.1090/S0002-9939-04-07065-0
PII:
S 0002-9939(04)07065-0
Received by editor(s):
April 17, 2002
Received by editor(s) in revised form:
September 25, 2002
Posted:
March 24, 2004
Communicated by:
Stephen D. Smith
Copyright of article:
Copyright
2004,
American Mathematical Society
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