Varieties generated by countably compact Abelian groups
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- by Dikran Dikranjan and Michael Tkachenko
- Proc. Amer. Math. Soc. 130 (2002), 2487-2496
- DOI: https://doi.org/10.1090/S0002-9939-02-06354-2
- Published electronically: February 4, 2002
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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.References
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Bibliographic Information
- Dikran Dikranjan
- Affiliation: Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100 Udine, Italy
- Email: dikranja@dimi.uniud.it
- Michael Tkachenko
- Affiliation: Departamento de Matemáticas, Universidad Autónoma Metropolitana, México
- MR Author ID: 190563
- Email: mich@xanum.uam.mx
- Received by editor(s): February 4, 2000
- Received by editor(s) in revised form: March 21, 2001
- Published electronically: February 4, 2002
- Additional Notes: The first author was partially supported by Research Grant of the Italian MURST in the framework of the project “Nuove prospettive nella teoria degli anelli, dei moduli e dei gruppi abeliani" 2000
The second author was partially supported by the Mexican National Council of Sciences and Technology (CONACyT), grant no. 400200-5-3012PE. He also thanks the hosts for the hospitality and generous support during his visit to the Università di Udine, Italy in December, 1999 - Communicated by: Alan Dow
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2487-2496
- MSC (1991): Primary 22A05, 22B05, 54D25, 54H11; Secondary 54A35, 54B30, 54D30, 54H13
- DOI: https://doi.org/10.1090/S0002-9939-02-06354-2
- MathSciNet review: 1897476