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On dense embeddings of discrete groups into locally compact groups


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.

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Correspondence to Maxim S. Boyko.

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Boyko, M.S., Gefter, S.L. & Kulagin, K.M. On dense embeddings of discrete groups into locally compact groups. Qual. Th. Dyn. Syst. 4, 31 (2003).

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Key words

  • locally compact groups
  • discrete groups
  • dense subgroups