convex l-lattice subgroups in l-ordered groups

In this paper, we have focused to study convex l-subgroups of an l-ordered group. first, we introduce the concept of a convex l-subgroup and a convex l-lattice subgroup of an l-ordered group and give some examples. then we find some properties and use them to construct convex l-subgroup generated by a subset s of an l-ordered group g . also, we generalize a well known result about the set of all convex subgroups of a lattice ordered group and prove that c(g), the set of all convex l-lattice subgroups of an l-ordered group g, is an l-complete lattice on height one. then we use these objects to construct the quotient l-ordered groups and state some related results.