Partial right orders on periodic extensions of abelian groups (Q5906371)

It is known that every semilinearly ordered nilpotent group is right-ordered [see \textit{S. V. Varaksin}, Algebra Logic 29, No. 6, 415-418 (1990; Zbl 0797.20028)]. In Theorem 1 it is shown that every semilinearly ordered group which is an extension of an abelian group by a periodic group is right-ordered. In Theorem 4 it is proven that every nonabelian soluble abelian-by-finite right-orderable group is not fully right-orderable. New examples of not fully right-orderable groups are also presented.