A note on just-non-Ω groups

Original Paper


Extending some previous notions in literature, we consider the class of just-non-Ω groups, where Ω is a prevariety of topological groups. Some structure theorems are shown in the compact case. We further analyze some concrete examples.


JNΩ groups Varieties and prevarieties of topological groups Lie groups 

Mathematics Subject Classification (2000)

22C05 20E22 20E34 


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  1. Bartholdi, L., Grigorchuk, R.: Lie methods in growth of groups and groups of finite width. Preprint (2000). arXiv:0002010v2 [math.GR]Google Scholar
  2. Caprace P.-E., Monod N.: Decomposing locally compact groups into simple pieces. Math. Proc. Cambridge Philos. Soc. 150, 97–128 (2011) arXiv:0811.4101 [math.GR]CrossRefMATHMathSciNetGoogle Scholar
  3. du Sautoy, M., Segal, D., Shalev, A.: New Horizons in Pro-p Groups. Progress in Mathematics, vol. 184. Birkhäuser, Boston (2000)Google Scholar
  4. Funar L., Otera D.E.: On the wgsc and qsf tameness conditions for finitely presented groups. Groups Geom. Dyn. 4(3), 549–596 (2010)CrossRefMATHMathSciNetGoogle Scholar
  5. Hofmann, K.H., Morris, S.A.: The Structure of Compact Groups. de Gruyter, Berlin (2006)Google Scholar
  6. Hofmann K.H., Morris S.A., Stroppel M.: Locally compact groups, residual Lie groups and varieties generated by Lie groups. Topol. Appl. 71, 63–91 (1996a)CrossRefMATHMathSciNetGoogle Scholar
  7. Hofmann K.H., Morris S.A., Stroppel M.: Varieties of topological groups, Lie groups, and SIN-groups. Colloq. Math. 70, 151–163 (1996)MATHMathSciNetGoogle Scholar
  8. Kurdachenko L., Otál J., Subbotin I.: Groups with Prescribed Quotient Subgroups and Associated Module Theory. World Scientific, Singapore (2002)Google Scholar
  9. Lennox J.C., Robinson D.J.: The Theory of Infinite Soluble Groups. Oxford University Press, Oxford (2004)CrossRefMATHGoogle Scholar
  10. Otera D.E.: On the simple connectivity at infinity of groups. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 6(3), 739–748 (2003)MATHMathSciNetGoogle Scholar
  11. Russo F.: On Compact just-non-Lie groups. J. Lie Theory 17(3), 625–632 (2007)MATHMathSciNetGoogle Scholar

Copyright information

© The Managing Editors 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PalermoPalermoItaly

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