Nonmeasurable subgroups of compact groups

Journal of Group Theory

Volumn 19, Issue 1, 2016, Pages 179-189

  Hernández, Salvador ^a   Hofmann, Karl H ^b   Morris, Sidney A ^c,d  

^a UNIVERSITAT JAUME I   (Spain)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^c UNIVERSITY OF BALLARAT   (Australia)

^d LA TROBE UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84954348641     PISSN: 14335883     EISSN: 14354446     Source Type: Journal    
DOI: 10.1515/jgth-2015-0034     Document Type: Article

References (31)

1. S. Berhanu, W.W. Comfort and J. D. Reid, Counting subgroups and topological group topologies, Pacific J. Math. 116 (1985), 217-241.
2. N. Bourbaki, Éléments de mathématique. VIII. Part. 1: Les structures fondamentales de l'analyse. Livre III: Topologie générale. Chap. 9: Utilisation des nombres réels en topologie générale. 2 iéme éd., Hermann, Paris, 1958.
3. N. Bourbaki, Éléments de mathématique. Fasc. XIII. Livre VI: Intégration. Chap. 1, 2, 3 et 4: Inégalités de convexite. Espaces de Riesz. Mesures sur les espaces localement compacts. Prolongement d'une mesure. Espaces Lp. 2ième éd. revue et augmentée, Hermann, Paris, 1965.
4. W. B. Brian and M.W. Mislove, Every compact group can have a non-measurable subgroups, preprint (2015), http://arxiv.org/abs/1503.01385v1.
5. W.W. Comfort, S. U. Raczkowski and F. J. Trigos-Arrieta, Making group topologies with, and without, convergent sequences, Appl. Gen. Topol. 7 (2006), 109-124.
6. M.V. Ferrer and S. Hernández, Dual topologies on non-abelian groups, Topology Appl. 159 (2012), 2367-2377.
7. P. Gartside and M. Smith, Counting the closed subgroups of profinite groups, preprint (2008), http://arxiv.org/abs/0809.4734.
8. B. R. Gelbaum, Problems in Real and Complex Analysis, Problem Books in Math., Springer, New York, 1992.
9. G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M.W. Mislove and D. S. Scott, Continuous Lattices and Domains, Encyclopedia Math. Appl. 93, Cambridge University Press, Cambridge, 2003.
10. J. E. Hart and K. Kunen, Compactifications of non-abelian groups, Topology Proc. 26 (2001-2002), 593-626.
11. S. Hernández, Questions raised at the conference "Algebra Meets Topology, " Barcelona, July 2010.
12. S. Hernández, K. H. Hofmann and S. A. Morris, The weights of closed subgroups of a locally compact group, J. Group Theory 15 (2014), 613-630.
13. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis. Vol. I: Structure of Topological Groups. Integration Theory. Group Representations, Grundlehren Math. Wiss. 115, Springer, Berlin, 1963.
14. K. H. Hofmann, Arc components of locally compact groups are Borel sets, Bull. Aust. Math. Soc. 65 (2002), 1-8.
15. K. H. Hofmann and S. A. Morris, A structure theorem on compact groups, Math. Proc. Cambridge Philos. Soc. 130 (2001), 409-426.
16. K. H. Hofmann and S. A. Morris, The Structure of Compact Groups, 3rd ed., De Gruyter Stud. Math. 25, De Gruyter, Berlin, 2013.
17. R. R. Kallman, Every reasonably sized matrix group is a subgroup of S1, Fund. Math. 164 (2000), 35-40.
18. A. B. Kharazishvili, On thick subgroups of uncountable β-compact locally compact commutative groups, Topology Appl. 156 (2009), 2364-2369.
19. A. Kleppner, Measurable homomorphisms of locally compact groups, Proc. Amer. Math. Soc. 106 (1989), 391-395.
20. D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, New York, 1955.
21. N. Nikolov and D. Segal, On finitely, generated profinite groups, I: Strong completeness and uniform bounds, Ann. of Math. (2) 165 (2007), 171-238.
22. H. L. Peterson, Extensions of Haar measure to relatively large nonmeasurable subgroups, Trans. Amer. Math. Soc. 228 (1977), 359-370.
23. L. Ribes and P. Zaleskii, Profinite Groups, 2nd ed., Springer, Berlin, 2000.
24. W. Rudin, Fourier Analysis on Groups, Interscience, New York, 1962.
25. W. Rudin, Principles of Mathematical Analysis, MacGraw-Hill, New York, 1953.
26. S. Saeki and K. Stromberg, Measurable subgroups and nonmeasurable characters, Math. Scand. 57 (1985), 359-374.
27. J. Saxl and J. S. Wilson, A note on popers in simple groups Math. Proc. Cambridge Philos. Soc. 122 (1997), 91-94.
28. M. G. Smith and J. S. Wilson On subgroups of finite index in compact Hausdorff groups, Arch. Math. 80 (2003), 123-129.
29. S. Thomas, Infinite products of finite simple groups II, J. Group Theory 2 (1999) 401-434.
30. Y. Zelenyuk, Ultrafilters and Topologies on Groups, De Gruyter Exp. Math. 50, De Gruyter, Berlin, 2011.
31. E. I. Zelmanov, On periodic compact groups, Israel J. Math. 77 (1992), 83-95.