On Baer's problem and properties of \(M''\)-groups (Q1409596)

In 1949, R. Baer raised the following question: If the group \(G\) is socle and for each \(\alpha<\gamma\) \(\text{Soc}_{\alpha+1}(G)/\text{Soc}_\alpha(G)\) is a direct product of finitely many minimal normal subgroups of\break \(G/\text{Soc}_\alpha(G)\), does it follow that \(G\) satisfies the minimal condition for normal subgroup? Later, in 1959, S. N. Chernikov motivated by this question raised his two problems regarding \(M''\)- and \(M'\)-groups. These questions have been answered in the negative by Ju. M. Mezebovskij (1972) and N. S. Chernikov (1991) independently. The article under review establishes new properties of \(M''\)-groups and contains new counterexamples to the problems of R. Baer and S. N. Chernikov.