Groups with subnormality for all subgroups that are not finitely generated
Groups in which every subgroup is subnormal have been studied extensively. The idea here is to study groups in which `most' of the subgroups are subnormal and the authors consider groups in which every subgroup which is not finitely generated is subnormal. They call these groups \(db\)-groups, being `dual' to Baer groups in which every finitely generated subgroup is subnormal. All groups with Max are \(db\)-groups including infinite simple groups with Max. To avoid these the authors restrict attention to locally finite groups and radical groups. An infinite locally finite \(db\)-group possessing non-subnormal subgroups is a Chernikov group and a complete description is given for this case. The main part of the paper leads to a satisfactory description of the radical \(db\)-groups.
scientific article; zbMATH DE number 878430
scientific article