Autour des groupes cycliquement ordonnés

— Cyclically ordered groups were introduced by Rieger, but the usual reference is the book of Fuchs, which is redacted in english. Other authors worked on cyclically ordered groups, one can note that they appear in MV-algebras and in some groups of permutations of chains. The first part of this expository paper is dedicated to definitions and well known properties. The second part deals with the first order theory of cyclically ordered groups, which was studied by M. Giraudet and F. Lucas. The third section studies rings of formal power series with exponents in a cyclically ordered group, and in the last one we define cyclically valued groups and cyclically ultrametric spaces and we focus on their first order theory.