Embeddings in Lattice-$O^*$-Groups

In the paper, the following results are obtained: the existence of simple divisible lattice-$O^*$-groups is established (Theorem 2.1) and it is proved that any countable lattice-orderable or right-orderable group can be isomorphically embedded in a simple divisible lattice-$O^*$-group (Theorem 2.2 and Corollary 2.3).