Abstract: Let G be an l group,П m(G)the set of its prime subgroups,П m(G)the set of its minimal prime subgroups ,P(G)the set of its polar subgroups ,C(G)the lattice of its convex l subgroups and Ω(G)the complete sublattice of C(G)generated by P(G).The elements of Ω(G)aredefined as the Ω subgroups of G.In this paper,the structure of lattice ordered groups was investigated with the help of their Ω subgroups .Some important new features of Lgroups were obtained and an important new description on the projectable l groups were given.Under the assumption that G is projectable we got the answer to the question:"when is C(G)=P?",which was proposed by P·Conrad.