Amenable Group - Properties

Properties

  • Every (closed) subgroup of an amenable group is amenable.
  • Every quotient of an amenable group is amenable.
  • A group extension of an amenable group by an amenable group is again amenable. In particular, finite direct product of amenable groups are amenable, although infinite products need not be.
  • Direct limits of amenable groups are amenable. In particular, if a group can be written as a directed union of amenable subgroups, then it is amenable.
  • Amenable groups are unitarizable; the converse is an open problem.
  • Countable discrete amenable groups obey the Ornstein isomorphism theorem.

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