ABSTRACT
In this article I wish to survey some diverse recent work on right ordered groups and (hopefully!) provide a coherent framework and account of it. Unlike the talk, I have tried to include more proofs to give some of the flavour and richness of the techniques used in the subject. All of the material covered is included in Chapters 2 & 6 of [Glass]. Recall that a group with a total
order defined on it is a right ordered group if xz < yz whenever x < y. Note that in any right ordered group, / > g if and only if fg~ l > 1; so it is enough to specify the elements of = {g Є G : g > 1} to define a right ordering on a group. All that is required is that G+ is a subsemigroup of G, and that G = G+ U G~ with G+ П G~ = {1} where G~ = {g Є G : g < 1}.
