Lattice ordered 2-divisible groups

In this work, we investigate some properties of a lattice ordered groups and norm function on this group and we recognize some special elements which is called admissible elements of a lattice ordered groups.Furthermore one can define a topology in a natural way on a lattice ordered group by norm function and a set C of admissible elements. Since this topology depends on the choice of the set C, we call this topology as C topology.If a lattice ordered group is 2-divisible and satisfies Archimedes? axiom then this group is a topological group with C topology.