Journal of the Australian Mathematical Society - Series A Vol. 64 Part 3 (1998) On groups in which every subgroup is subnormal of defect at most three Gunnar Traustason Christ Church Oxford OX1 1DP England e-mail: traustas ermine.ox.ac.uk Abstract: 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 subnormal of defect at most 3 if and only if G is nilpotent of class at most 3. When G is of exponent 7the situation is different. While every 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 such groups with class exactly 4. We also investigate the structure of these groups. PDF file size: 129K © Copyright 1998, Australian Mathematical Society