On fully quasitransitive abelian groups

We describe fully quasitransitive torsion-free groups in the class of groups whose endomorphism ring is a skew field as well as in the class of groups that are direct sums of homogeneous groups. We prove the full transitivity of fully quasitransitive cohesive groups and the quasitransitive torsion-free groups coinciding with their pseudosocle and having $p$-rank $\le1$ for each prime $p$.