ABELIAN-BY-NILPOTENT GROUPS WITH CHAIN CONDITIONS FOR NORMAL SUBGROUPS OF INFINITE ORDER OR INDEX Paek, Dae-Hyun;
Abstract
We study the structure of abelian-by-nilpotent groups satisfying the maximal condition on infinite normal subgroups or the minimal condition on normal subgroups of infinite index.
METANILPOTENT GROUPS WITH CHAIN CONDITIONS FOR NORMAL SUBGROUPS OF INFINITE ORDER OR INDEX,;
대한수학회보, 2008. vol.45. 1, pp.105-109
References
1.
M. Karbe, Groups satisfying the weak chain conditions for normal subgroups, Rocky Mountain J. Math. 17 (1987), no. 1, 41-47
2.
L. A. Kurdachenko, Groups that satisfy weak minimality and maximality conditions for normal subgroups, Sibirsk. Mat. Zh. 20 (1979), no. 5, 1068-1076, 1167
3.
F. De Giovanni, D. H. Paek, D. J. S. Robinson, and A. Russo, The maximal and minimal conditions for normal subgroups of infinite order or index, Comm. Algebra 33 (2005), no. 1, 183-199
4.
D. H. Paek, Locally nilpotent groups with the maximal condition on infinite normal subgroups, Bull. Korean Math. Soc. 41 (2004), no. 3, 465-472
5.
D. H. Paek, Locally nilpotent groups with the minimal condition on normal subgroups of infinite index, Bull. Korean Math. Soc. 41 (2004), no. 4, 779-783
6.
D. J. S. Robinson, Finiteness conditions and generalized soluble groups, Springer-Verlag, Berlin, 1972
7.
D. J. S. Robinson, A course in the theory of groups, Graduate Texts in Mathematics, 80. Springer- Verlag, New York, 1996