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On the minimality of powers of minimal  -bounded abelian groups
Author(s):
Dikran
Dikranjan;
Alberto
Tonolo
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3101-3110.
MSC (1991):
Primary 54F45, 54D05, 54D30;
Secondary 22A05, 22D05, 54D25
Posted:
April 23, 1999
MathSciNet review:
1600132
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Abstract:
We describe the structure of totally disconnected minimal  -
bounded abelian groups by reducing the description to the case of those of them which are subgroups of powers of the  -adic integers  . In this case the description is obtained by means of a functorial correspondence, based on Pontryagin duality, between topological and linearly topologized groups introduced by Tonolo. As an application we answer the question (posed in Pseudocompact and countably compact abelian groups: Cartesian products and minimality, Trans. Amer. Math. Soc. 335 (1993), 775-790) when arbitrary powers of minimal  -bounded abelian groups are minimal. We prove that the positive answer to this question is equivalent to non-existence of measurable cardinals.
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Additional Information:
Dikran
Dikranjan
Affiliation:
Dipartimento di Matematica e Informatica, Udine University, via delle Scienze 206 (località Rizzi), 33100 Udine, Italy
Email:
dikranja@dimi.uniud.it
Alberto
Tonolo
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Padova University, Via Belzoni 7, 35131 Padova, Italy
Email:
tonolo@math.unipd.it
DOI:
10.1090/S0002-9939-99-04834-0
PII:
S 0002-9939(99)04834-0
Keywords:
Totally disconnected group,
connected group,
countably compact group,
$\omega $-bounded group,
minimal group,
measurable cardinal
Received by editor(s):
March 25, 1997
Received by editor(s) in revised form:
December 13, 1997
Posted:
April 23, 1999
Communicated by:
Alan Dow
Copyright of article:
Copyright
1999,
American Mathematical Society
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