(Totally) L-ordered Groups

In this paper, first we investigate some properties of L-ordered groups such as L-subgroup generated by an arbitrary subset and product of L-ordered groups. Then we introduce the notions of totally L-ordered group and strong totally L-ordered group, where L is a frame and some related results are obtained. We show that the set of all isomorphisms on a totally L- subgroup, forms an L-ordered group. Moreover, if it is a strong totally L-ordered group, then the set of all isomorphisms on it is an L-lattice ordered group.