Homogeneous Cayley objects

We examine a number of countable homogeneous relational structures with the aim of determining which countable groups can act regularly on them. Since a group X acts regularly on a graph G if and only if G is a Cayley graph for X, we will extend the terminology and say that M is a Cayley object for X if X acts regularly on M. We consider, among other things, graphs, hypergraphs, metric spaces and total orders. (C) 2000 Academic Press.