Multiplication groups of quotient divisible abelian groups (Q6607134)

The reviewed paper deals with a study of the multiplication groups of quotient divisible abelian groups. In fact, studying the relationship between properties of a ring and the structure of its additive group has a long history in the contemporary algebra and attracts the interest of many of the modern-day algebraists.\N\NConcretely, the work is devoted to the investigation of multiplication groups of quotient divisible Abelian groups. A group \(G\) is said to be \textit{quotient divisible} if it does not contain non-zero divisible torsion subgroups, but contains a free finite-rank subgroup \(F\) such that the factor-group \(G/F\) is a divisible torsion group. The concept of a quotient divisible group was introduced by \textit{R. A. Beaumont} and \textit{R. S. Pierce} [Ill. J. Math. 5, 61--98 (1961; Zbl 0108.03802)] to describe groups admitting a ring structure that is embedded in a semi-simple separable algebra. This notion was non-trivially extended to the case of mixed Abelian groups by \textit{A. Fomin} and \textit{W. Wickless} [Proc. Am. Math. Soc. 126, No. 1, 45--52 (1998; Zbl 0893.20041)], where it is shown that mixed quotient divisible groups are dual to torsion-free Abelian groups of finite rank.\N\NThe article is well-written and structured as the main results are stated and proved in Theorems 2.1,2.2; 3.1,3.2,3.3; 4.1,4.2, respectively.\N\NThis is really a serious exploration which will be of substantial interest for the commutative group-theoretic community.