Relative minimality and co-minimality of subgroups in topological groups

Topology and its Applications

Volumn 157, Issue 1, 2010, Pages 62-76

  Dikranjan, Dikran ^a   Megrelishvili, Michael ^b  

^a UNIVERSITY OF UDINE   (Italy)

^b BAR ILAN UNIVERSITY   (Israel)

Author keywords

Co minimal subgroup; Heisenberg group; Minimal group; Relatively minimal subgroup

Indexed keywords

EID: 70350147288     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2009.04.048     Document Type: Article

References (23)

1. L. Außenhofer, M.J. Chasco, D. Dikranjan, X. Dominguez, Locally minimal topological groups, in preparation
2. Banakh T. Locally minimal topological groups and their embeddings into products of o-bounded groups. Comment. Math. Univ. Carolin. 41 4 (2000) 811-815
3. Dierolf S., and Schwanengel U. Examples of locally compact non-compact minimal topological groups. Pacific J. Math. 82 (1979) 349-355
4. Dikranjan D. Recent progress in minimal topological groups. Topology Appl. 85 (1998) 53-91
5. Dikranjan D., and Giordano Bruno A. Arnautov's problems on semitopological isomorphisms. Appl. Gen. Topol. 10 1 (2009) 85-119
6. Dikranjan D., and Morris S. Subgroups of products of locally compact groups. Proceedings of the 16th Summer Conference on General Topology and its Applications (New York). Topology Proc. 26 2 (2001/2002) 533-544
7. Dikranjan D., and Prodanov Iv. Totally minimal groups. Annuaire Univ. Sofia Fac. Math. Méc. 69 (1974/1975) 5-11
8. Dikranjan D., Prodanov Iv., and Stoyanov L. Topological Groups: Characters, Dualities and Minimal Group Topologies. Pure Appl. Math. vol. 130 (1989), Marcel Dekker, New York, Basel
9. Dikranjan D., Tkachenko M., and Yaschenko Iv. On transversal group topologies on non-abelian groups. Topology Appl. 153 17 (2006) 3338-3354
10. Doïtchinov D. Produits de groupes topologiques minimaux. Bull. Sci. Math. (2) 97 (1972) 59-64
11. Eberhardt V., Dierolf S., and Schwanengel U. On products of two (totally) minimal topological groups and the three-space-problem. Math. Ann. 251 (1980) 123-128
12. Megrelishvili M. Group representations and construction of minimal topological groups. Topology Appl. 62 (1995) 1-19
13. Megrelishvili M. G-minimal topological groups. Abelian Groups, Module Theory and Topology. Lect. Notes Pure Appl. Math. vol. 201 (1998), Marcel Dekker 289-300
14. Megrelishvili M. Generalized Heisenberg groups and Shtern's question. Georgian Math. J. 11 4 (2004) 775-782
15. Megrelishvili M. Every topological group is a group retract of a minimal group. Topology Appl. 155 (2008) 2105-2127
16. Milnes P. Enveloping semigroups, distal flows and groups of Heisenberg type. Houston J. Math. 15 4 (1989) 563-572
17. Morris S., and Pestov V. On Lie groups in varieties of topological groups. Colloq. Math. 78 1 (1998) 39-47
18. Reiter H. Uber den Satz von Wiener and lokalkompakte Gruppen. Comment. Math. Helv. 49 (1974) 333-364
19. M. Shlossberg, Minimality on topological groups and Heisenberg type groups, Topology Proc., in press
20. Remus D., and Stoyanov L. Complete minimal topological groups. Topology Appl. 42 (1991) 57-69
21. Schwanengel U. An example of a q-minimal precompact topological group containing a non-minimal closed normal subgroup. Manuscripta Math. 27 (1979) 323-327
22. Stephenson R. Minimal topological groups. Math. Ann. 192 (1971) 193-195
23. Uspenskij V.V. On subgroups of minimal topological groups. Topology Appl. 155 (2008) 1580-1606