• Corpus ID: 249926554

Subsets of Virtually Nilpotent Groups with the SBM Property

  title={Subsets of Virtually Nilpotent Groups with the SBM Property},
  author={Ryan Burkhart and Isaac Goldbring},
. We extend Leth’s notion of subsets of the integers satisfying the Standard interval measure (SIM) property to the class of virtually nilpotent groups and name the corresponding property the Standard ball measure (SBM) property. In order to do this, we define a natural measure on closed balls in asymptotic cones associated to such groups and show that this measure satisfies the Lebesgue density theorem. We then prove analogs of various properties known to hold for SIM sets in this broader… 



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  • M. Sapir
  • Mathematics
    Int. J. Algebra Comput.
  • 2015
It is shown how a recent result of Hrushovsky implies that if an asymptotic cone of a finitely generated group is locally compact, then the group is virtually nilpotent.