%0 Journal Article %T Convex $L$-lattice subgroups in $L$-ordered groups %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Borzooei, Rajabali %A Hosseini, Fateme %A Zahiri, Omid %D 2018 %\ 07/01/2018 %V 9 %N 1 %P 139-161 %! Convex $L$-lattice subgroups in $L$-ordered groups %K $L$-ordered group %K convex $L$-subgroup %K (normal) convex $L$-lattice subgroup %R 10.29252/cgasa.9.1.139 %X 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. %U https://cgasa.sbu.ac.ir/article_50748_0ee3783313053dea8791d1990de4c8e2.pdf