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We introduce right generating sets, Cayley graphs, growth functions, typesand rates, and isoperimetric constants for left homogeneous spaces equippedwith coordinate systems; characterise right amenable finitely right generatedleft homogeneous spaces with finite stabilisers as those whose isoperimetricconstant is $0$; and prove that finitely right generated left homogeneousspaces with finite stabilisers of sub-exponential growth are right amenable, inparticular, quotient sets of groups of sub-exponential growth by finitesubgroups are right amenable.

Right Amenability And Growth Of Finitely Right Generated Left Group Sets