Right Amenability And Growth Of Finitely Right Generated Left Group Sets
  We introduce right generating sets, Cayley graphs, growth functions, types
and rates, and isoperimetric constants for left homogeneous spaces equipped
with coordinate systems; characterise right amenable finitely right generated
left homogeneous spaces with finite stabilisers as those whose isoperimetric
constant is $0$; and prove that finitely right generated left homogeneous
spaces with finite stabilisers of sub-exponential growth are right amenable, in
particular, quotient sets of groups of sub-exponential growth by finite
subgroups are right amenable.
