Supramenable groups

In this thesis we investigate the class of supramenable groups. In the first part we give an overview of some analogous characterizations of amenable and supramenable groups. This is followed by the study of two properties close to supramenability: megamenability, which is a stronger property, and a Reiter condition that turns out to be equivalent to sub-exponential growth. In chapter three we present an argument showing why supramenable groups are precicely the groups not admitting an injective Lipschitz embedding of a free group. In the fourth and last chapter we give a characterization by a measure property before concluding with a fixed point property.