On the minimality of powers of minimal 𝜔-bounded abelian groups

Dikranjan, Dikran; Tonolo, Alberto

doi:10.1090/S0002-9939-99-04834-0

On the minimality of powers of minimal $\omega$-bounded abelian groups
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by Dikran Dikranjan and Alberto Tonolo PDF

Proc. Amer. Math. Soc. 127 (1999), 3101-3110 Request permission

Abstract:

We describe the structure of totally disconnected minimal $\omega$- bounded abelian groups by reducing the description to the case of those of them which are subgroups of powers of the $p$-adic integers $\mathbb {Z}_{p}$. 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 $\omega$-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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