Groups satisfying the minimal condition on subgroups which are not transitively normal (Q2120271)

A subgroup \(X\) of a group \(G\) is transitively normal, if \(X\) is normal in every subgroup \(Y \geq H\) in which \(X\) is subnormal. The main result proved in the paper under review is: Let \(G\) be a group satisfying the minimal condition on subgroups which are not transitively normal. If \(G\) has no infinite simple sections, then either \(G\) is Chernikov or all subgroups of \(G\) are transitively normal. In particular, if \(G\) is not periodic, then it is abelian.