On a class of separable Dedekind groups (Q2754824)

A class of generalized Dedekind groups is described (a Dedekind group is a group in which all subgroups are normal). The author considers locally solvable groups \(G\) with the following restriction on the system of subgroups: all infinite subgroups of \(G\) which are not contained in a fixed proper subgroup \(S\subset G\) are normal (they are denoted as \(H(I\setminus S)\)-groups). It is shown that such groups are either so-called \(H(S)\)-groups (in which all subgroups not contained in \(S\) are normal) or are some extensions of products of quasicyclic groups by \(H(S)\)-groups.