Groups with Tarski number 5

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The Tarski number of a non-amenable group G is the minimal number of pieces in a paradoxical decomposition of G. Until now the only numbers which were known to be Tarski numbers of some groups were 4 and 6. We construct a group with Tarski number 5 and mention a related result for Tarski numbers of group actions.
Original languageEnglish
JournalAdvances in Mathematics
StatePublished - 2014


  • math.GR


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