Shalom’s property HFD and extensions by ℤ of locally finite groups

  • Jérémie BrieusselEmail author
  • Tianyi Zheng


We show that every finitely generated extension by ℤ of a locally normally finite group has Shalom’s property HFD. The statement is no longer true without the normality assumption. This permits to answer some questions of Shalom, Erschler–Ozawa and Kozma. We also obtain a Neumann–Neumann embedding result that any countable locally finite group embeds into a two-generated amenable group with property HFD.


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© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Institut Montpelliérain Alexander GrothendieckUniversité de MontpellierMontpellierFrance
  2. 2.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

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