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http://dx.doi.org/10.4134/BKMS.2004.41.4.779

LOCALLY NILPOTENT GROUPS WITH THE MINIMAL CONDITION ON NORMAL SUBGROUPS OF INFINITE INDEX  

Paek, Dae-Hyun (Department of Mathematics Education, Busan National University of Education)
Publication Information
Bulletin of the Korean Mathematical Society / v.41, no.4, 2004 , pp. 779-783 More about this Journal
Abstract
A group G is said to satisfy the minimal condition on normal subgroups of infinite index if there does not exist an infinite properly descending chain $G_1$ > $G_2$ > ... of normal subgroups of infinite index in G. We characterize the structure of locally nilpotent groups satisfying this chain condition.
Keywords
locally nilpotent groups; minimal condition on infinite normal subgroups of infinite index;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 L. A. Kurdacenko, Groups satisfying weak minimum and maximum conditions for normal subgroups, Sibirsk. Mat. Zh. Z. 20 (1979), 1068–1076. [Trans: Siberian Math. J. 20 (1980), 755–761.]
2 L. A. Kurdacenko, Locally nilpotent groups with a weak minimality condition for normal subgroups, Sibirsk. Mat. Zh. Z. 25 (1984), 99–106. [Trans: Siberian Math. J. 25 (1985), 589–594.]
3 D. H. Paek, Chain conditions for subnormal subgroups of infinite order or index, Comm. Algebra 29 (2001), 3069–3081
4 D. H. Paek, Chain conditions for subgroups of infinite order or index, J. Algebra 249 (2002), 291–305
5 D. H. Paek, Locally nilpotent groups with the maximal condition on infinite normal subgroups, Bull. Korean Math. Soc. 41 (2004), no. 3, 465–472
6 D. J. S. Robinson, Finiteness Conditions and Generalized Soluble Groups (1972), Springer-Verlag, Berlin
7 D. J. S. Robinson, A Course in the Theory of Groups (1995), Springer-Verlag, New York