Varieties generated by countably compact Abelian groups

Dikranjan, Dikran; Tkachenko, Michael

doi:10.1090/S0002-9939-02-06354-2

Varieties generated by countably compact Abelian groups
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Proc. Amer. Math. Soc. 130 (2002), 2487-2496 Request permission

Abstract:

We prove under the assumption of Martin’s Axiom that every precompact Abelian group of size $\leq 2^{\aleph _0}$ belongs to the smallest class of groups that contains all Abelian countably compact groups and is closed under direct products, taking closed subgroups and continuous isomorphic images.

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