On dense embeddings of discrete groups into locally compact groups

  • Maxim S. Boyko
  • Sergey L. Gefter
  • Konstantin M. Kulagin


We consider a class of discrete groups which have no ergodic actions by translations on continuous non-compact locally compact groups. We also study dense embeddings ofZ n (n>1) into non-compact locally compact groups. Moreover, we study some discrete groups which admit no embeddings into almost connected locally compact groups. In particular, we prove that a lattice in a simple Lie group with property (T) cannot be embedded densely into a connected non-compact locally compact group.

Key words

locally compact groups discrete groups dense subgroups 


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Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  • Maxim S. Boyko
    • 1
  • Sergey L. Gefter
    • 1
  • Konstantin M. Kulagin
    • 1
  1. 1.Institute for Low Temperature Physics and EngineeringKharkovUkraine

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