On Groups Saturated with Abelian Subgroups

Groups with the weak maximal condition on non-abelian subgroups are the main subject of this research. Locally finite groups with this property are abelian or Chemikov. Non-abelian groups with the weak maximal condition on non-abelian subgroups, which have an ascending series of normal subgroups with locally nilpotent or locally finite factors, are described in this article.