This paper deals with the invariant sets in the group of isometries of a lattice-ordered group. It is shown that all the invariant sets are union of some transitivity subsets of the spheres.
@article{urn:eudml:doc:38966, title = {Invariant sets in the group of isometries of a lattice-ordered group.}, journal = {Stochastica}, volume = {5}, year = {1981}, pages = {163-167}, zbl = {0565.06014}, mrnumber = {MR0659247}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38966} }
Grané Manlleu, Josep. Invariant sets in the group of isometries of a lattice-ordered group.. Stochastica, Tome 5 (1981) pp. 163-167. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38966/