Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58539120180701Convex $L$-lattice subgroups in $L$-ordered groups13916150748ENRajabali BorzooeiDepartment of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran.Fateme HosseiniDepartment of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran.Omid ZahiriUniversity of Applied Science and Technology, Tehran, IranJournal Article20170326In 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.http://cgasa.sbu.ac.ir/article_50748_0ee3783313053dea8791d1990de4c8e2.pdf