CINECA IRIS Institutional Research Information System
IRIS è la piattaforma adottata dall’Università degli Studi di Udine per gestire l’archivio aperto dei prodotti della ricerca. L’archivio contiene articoli, contributi in volume, monografie, interventi pubblicati in atti di convegno, Tesi di dottorato e altri materiali.
EnglishEvery proper closed subgroup of a connected Hausdorff group must have index at least c, the cardinality of the continuum. 70 years ago Markov conjectured that a group G can be equipped with a connected Hausdorff group topology provided that every subgroup of G which is closed in all Hausdorff group topologies on G has index at least c. Counter-examples in the non-abelian case were provided 25 years ago by Pestov and Remus, yet the problem whether Markov's Conjecture holds for abelian groups G remained open. We resolve this problem in the positive.
| Titolo: | A complete solution of Markov's problem on connected group topologies |
| Autori: | |
| Data di pubblicazione: | 2016 |
| Rivista: | |
| Abstract: | Every proper closed subgroup of a connected Hausdorff group must have index at least c, the cardinality of the continuum. 70 years ago Markov conjectured that a group G can be equipped with a connected Hausdorff group topology provided that every subgroup of G which is closed in all Hausdorff group topologies on G has index at least c. Counter-examples in the non-abelian case were provided 25 years ago by Pestov and Remus, yet the problem whether Markov's Conjecture holds for abelian groups G remained open. We resolve this problem in the positive. |
| Handle: | http://hdl.handle.net/11390/1069907 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| ConnectedMarkov-revision2-2.pdf | Articolo principale | Post-print |  | Embargo: 01/01/2020 Richiedi una copia |
http://hdl.handle.net/11390/1069907
Copyright © 2018