Soluble groups with few non-Baer subgroups. (Q1421088)

The author describes the consequences for a group to satisfy a chain condition for its non-Baer subgroups. A soluble not finitely generated group satisfying the maximum condition for non-Baer subgroups is still locally nilpotent and a product of a normal subgroup \(L\) with a polycyclic subgroup \(U\) such that \(L'U\) is a Baer subgroup, with some further conditions (see Theorem 1). A non-Baer group which is soluble and satisfies the minimum condition for non-Baer subgroups is a Chernikov group (compare Theorem 2).