caa a22 4500 388046864 CHVBK 20180307125040.0 cr unu---uuuuu 161130e199806 xx s 000 0 eng 10.1017/S1446788700039240 doi S1446788700039240 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700039240 Traustason Gunnar Christ Church Oxford OX1 1DP England e-mail: traustas@ermine.ox.ac.uk On groups in which every subgroup is subnormal of defect at most three [Elektronische Daten] [Gunnar Traustason] 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 7 the 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. Copyright © Australian Mathematical Society 1998 primary 20F19 nationallicence 20F45 nationallicence secondary 20F18 nationallicence Journal of the Australian Mathematical Society Cambridge University Press 64/3(1998-06), 397-420 1446-7887 64:3<397 1998 64 JAZ https://doi.org/10.1017/S1446788700039240 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700039240 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Traustason Gunnar Christ Church Oxford OX1 1DP England e-mail: traustas@ermine.ox.ac.uk NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 64/3(1998-06), 397-420 1446-7887 64:3<397 1998 64 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge