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.

Read more about this topic:  Amenable Group

Famous quotes containing the word properties:

    “A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
    —Ralph Waldo Emerson (1803–1882)

    “The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
    —John Locke (1632–1704)