Abstract
We study locally nilpotent groups containing subgroups of classc, c>1, and satisfying the weak maximum condition or the weak minimum condition on c-nilpotent subgroups. It is proved that nilpotent groups of this type are minimax and periodic locally nilpotent groups of this type are Chernikov groups. It is also proved that if a group G is either nilpotent or periodic locally nilpotent and if all of its c-nilpotent subgroups are of finite rank, then G is of finite rank. If G is a non-periodic locally nilpotent group, these results, in general, are not valid.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 384–389, March, 1992.
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Onishchuk, V.A., Sysak, Y.P. Locally nilpotent groups satisfying the weak minimum or maximum condition for subgroups of bounded nilpotency class. Ukr Math J 44, 334–337 (1992). https://doi.org/10.1007/BF01063134
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DOI: https://doi.org/10.1007/BF01063134