ON GROUPS IN WHICH EVERY SUBGROUP IS SUBNORMAL OF DEFECT AT MOST 3

In this paper we study groups in which every subgroup is subnormal of defect at most 3. Let G be a group which is either torsion-free or of prime exponent different from 7. We show that every subgroup in G is s ubnormal of defect at most 3 if and only if G is nilpotent of class at most 3. When G is of exponent 7 the situation is different. While eve ry group of exponent 7, in which every subgroup is subnormal of defect at most 3, is nilpotent of class at most 4, there are examples of suc h groups with class exactly 4. We also investigate the structure of th ese groups.