Convex L-lattice subgroups in L-ordered groups

In this paper, we have focused to study convex L-subgroups of an Lordered 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.